Answers
The sum of the perimeters of all squares is 80 ft.
What is perimeter?
Perimeter is the distance around the outer boundary of a two-dimensional shape, such as a rectangle, square, triangle, or circle. It is the total length of all the sides of the shape.
Starting with a square with a perimeter of 40 ft, we can find the length of one side by dividing the perimeter by 4:
[tex]\frac{40ft}{4} = 10ft[/tex]
So, the original square has a side length of 10 ft.
Connecting the midpoints of the sides of this square creates a new square with half the side length of the original square. Each side of this new square is the hypotenuse of a right triangle with legs equal to half the side length of the original square (i.e., 5 ft).
Using the Pythagorean theorem, we can find the length of each side of the new square:
[tex]s^2 = (5 ft)^2 + (5 ft)^2[/tex]
[tex]s^2 = 50 ft^2[/tex]
[tex]s = \sqrt{50}ft[/tex]
So, the second square has a side length of [tex]\sqrt{50}ft[/tex], which is approximately 7.07 ft.
Continuing this process, each subsequent square will have half the side length of the previous square. Therefore, the side length of the third square will be half the side length of the second square, which is:
[tex]\frac{1}{2}[/tex] * [tex]\sqrt{50}ft[/tex] = [tex]\sqrt{25}ft[/tex] = 5 ft.
The side length of the fourth square will be half the side length of the third square, which is: [tex]\frac{1}{2}[/tex] * 5 ft = 2.5 ft. And so on.
The perimeters of the squares are:
The perimeter of the first square is 40 ft.
The perimeter of the second square is 4 * [tex]\sqrt{50}ft[/tex], which is approximately 28.28 ft.
The perimeter of the third square is 4 * 5 ft = 20 ft.
The perimeter of the fourth square is 4 * 2.5 ft = 10 ft.
We can see that the perimeter of each subsequent square is half the perimeter of the previous square. So, the series for the perimeters of the squares is a geometric series with a first term of 40 ft and a common ratio of 1/2.
Using the formula for the sum of an infinite geometric series, we can find the sum of the perimeters of all squares:
S = a / (1 - r)
where a is the first term (40 ft) and r is the common ratio (1/2). Plugging in these values, we get:
S = 40 ft / (1 - 1/2)
S = 80 ft
Therefore, the sum of the perimeters of all squares is 80 ft.
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Related Questions
Orlando skipped rope 135 times in 45 seconds.Assuming a constant rate how many time Orlando skip rope per second
Answers
Answer: 3 times per second
Step-by-step explanation:
Orland skipped 135 times in 45 seconds, so you divide 135/45 which is 3, so it is 3 skips per second :)
hope this helped <33
Roberto will put a border around the edges of the platform how much border will he need if the area is 12 square units?
Answers
The amount of border that Roberto will need to put around the edges of the platform, given the area is 16 units.
How to find the amount of border ?The platform is given in the figure and to find the amount of border that Roberto needs to cover it if the area is 12 square units, you need to count the number of dots all along the edges of the platforms.
Counting this would give us 16 dots. This then means that Roberto needs sixteen units of border to be able to put up a border around the edges of the platform.
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Dima has twice as many books as Ramiro. If dima gives 12 books to Ramiro, they will have the same number of books.How many books do they have in total
Answers
Answer:
They have 36 books in total.
Step-by-step explanation:
Let d = The number of Dima's books
Let r = The number of Ramiro's books.
d = 2r
d - 12 = r Substitute 2r for d in the second equation and solve for r
2r - 12 = r Subtract 2r from both sides
2r - 2r - 12 = r - 2r
-12 = -r Multiply both sides by -1
12 = r
Ramiro has 12 books.
d = 2r substitute 12 for r and solve for d
d = 2(12)
d = 24
Dima has 24 books.
Together they have 36 books (12 + 24)
Helping in the name of Jesus.
Answer:36
Step-by-step explanation:
Solomon is taking out a $18,320, two-year loan with an APR of 3.29%. What will be the finance charge for this loan to the nearest dollar?
Answers
$634.43 is the finance charge/ the interest on the loan.
Tell whether the triangle with the given side lengths is a right triangle. 45 in., 26 in., 51 in.
Answers
A it is nearly but not a right angled triangle.
Step-by-step explanation:
I used pythagorous theorum.
Answer:
No it is not
Step-by-step explanation:
Hypotenuse is the longest side
A ² = B² + C² (Using Pythagoras theorem)
51² = 45² + 26²
2601 =2025 +676
2601 = 2701
This is not a right angle triangle
Square root of 2701 is 51.57 and that is equivalent to 52
Directions: Work in your small group to complete this worksheet Submit the completed Wor full credit. Canvas by the beginning of the next class. All answers must be justified and work Trigonometric functions are periodic, meaning they repeat the same pattern as x goes toward positive and negative infinity. Hence, trigonometric functions fail to be one to one. Recall, one to one functions must pass BOTH vertical and horizontal line tests. Therefore, to define the trigonometric inverse functions, we must restrict the domain of each trigonometric function to a place where the function IS one to one. 1. Let g(x) be the function whose domain is [0,π] and whose outputs are determined by cos(x) on this interval. Hence, g(x) is the solid line part of the graph pictured to the right. Note: g(x) is defined in terms of cos(x), however g(x)=cos(x) since it has a different domain. a) Does y=cos(x) have an inverse function? Why or why not? b) Explain why g(x) has an inverse function, g−1(x)=cos−1(x). c) State the domain and range of g(x) in interval notation. Domain: Range: d) State the domain and range of g−1(x)=cos−1(x) in interval notation. Domain: Range:
Answers
a)Does not have an inverse function
b) g(x) has an inverse function
c)Domain of g(x) is [0, π],range is [-1, 1]
d)domain of g−1(x)=cos−1(x) is [-1, 1], range is [0, π]
a) No, y=cos(x) does not have an inverse function because it fails the vertical line test.
b) g(x) has an inverse function, g−1(x)=cos−1(x), because it passes the vertical and horizontal line tests when its domain is restricted to the interval [0, π].
c) The domain of g(x) is [0, π], and the range is [-1, 1] in interval notation.
d) The domain of g−1(x)=cos−1(x) is [-1, 1], and the range is [0, π] in interval notation.
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Evaluate : x = 3 , y = -6 then
4y - 6x = xy?
Answers
"Substituting x = 3 and y = -6 in the given equation, we get:
4y - 6x = xy
4(-6) - 6(3) = (3)(-6)
-24 - 18 = -18
-42 ≠ -18
Therefore, the given equation is not true for x = 3 and y = -6." (ChatGPT, 2023)
Find the length of an edge of a square whose diagonals are of length 10cm
Answers
Answer:
Step-by-step explanation:
Diagonals intersect at 90°.
[tex]x^2=5^2+5^2[/tex] (Pythagoras Theorem)
[tex]=50[/tex]
[tex]x=\sqrt{50}[/tex] cm =7.07 cm
7.07 cm
Step by step explanation:
Let's use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In a square, the diagonals are the longest sides and they are equal in length. Let x be the length of one of the sides of the square, then we can use the Pythagorean theorem to find x:
(diagonal)^2 = (side)^2 + (side)^2
10^2 = x^2 + x^2 (since the diagonal is the hypotenuse of a right triangle formed by the two sides of the square)
100 = 2x^2
x^2 = 50
x = sqrt(50) = 5 * sqrt(2)
Therefore, the length of an edge of the square is 5 * sqrt(2) cm (approximately 7.07 cm to two decimal places).
You are enclosing a circluar flower graden with a fence that cost $2. 99 per foot. The radius of a garden is 7 feet. How much will it cost to buy the fence
Answers
Answer: 20.93
Step-by-step explanation:
2.99x7
(Please answer quickly!!!!)Simplify the expression.
−9.71 + 2.8
−12.61
−9.73
−6.91
69.10
Answers
Answer:
Step-by-step explanation:
−9.71 + 2.8 = -6.91
Answer:
6.91.
9.71
2.8
6.1
if you subtract 9.71 from 2.8 keep everything in point
QUESTION 6 Any square matrix multiplied by its inverse will be that size identity matrix.
Answers
Given statement: "Any square matrix multiplied by its inverse will be that size identity matrix."
The statement is correct because for a square matrix A, if it is multiplied by its inverse, we get the identity matrix of the same order. The product of the matrix with its inverse is commutative.
The identity matrix is a square matrix with 1's along the diagonal and 0's elsewhere. For example, the 3x3 identity matrix is shown below.
1 0 0
0 1 0
0 0 1
The inverse of a square matrix A is a matrix A^-1, such that AA^-1 = A^-1A = I, where I is the identity matrix.
For example, let us consider a 2x2 matrix A. A = (a, b, c, d)
The inverse of the matrix A is given by the formula. A^-1 = 1/(ad-bc) * (d, -b, -c, a)
Thus, AA^-1 = A^-1A = I, where I is a 2x2 identity matrix. Therefore, any square matrix multiplied by its inverse will be that size identity matrix.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answers
The sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT ( option C)
What Is sample space ?The sample space of a random experiment is the collection of all possible outcomes.
When we toss a coin, there can be only two outcomes i.e., either head or tail. So, the sample space will be, S = {H, T} where H is the head and T is the tail.
When Ted tossed the coin three times, the sample space include;
TTT, TTH, THT, HHH, HHT, HTH, THH, HTT
This means the total sample space is 8.
Therefore the sample space for Ted's experiment is TTT, TTH, THT, HHH, HHT, HTH, THH, HTT
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alice, bob and carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. the simplest common denominator of alice's and bob's expressions is 4x2. the simplest common denominator of bob's and carol's expressions is 12x3. the simplest common denominator of alice and carol's expressions is 6x3. find all possible expressions that could be carol's
Answers
All possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 .
Alice, Bob and Carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of x as the denominator. The simplest common denominator of Alice's and Bob's expressions is 4x2, while the simplest common denominator of Bob's and Carol's expressions is 12x3. The simplest common denominator of Alice's and Carol's expressions is 6x3. To explain further, Alice's expression can be any fraction with 1 as the numerator and a constant integer times x2 as the denominator, therefore, the denominator of Alice's expression can be any multiple of 4, i.e. 4x2, 8x2, 12x2, 16x2, 20x2 and so on.
Bob's expression can also be any fraction with 1 as the numerator and a constant integer times x2 as the denominator. However, the denominator of Bob's expression must be a multiple of both 4 and 6, i.e. 12x2, 24x2, 36x2, 48x2 and so on. Therefore, Carol's expression must be in the form of a fraction with 1 as the numerator and a constant integer times x3 as the denominator. This means that the denominator of Carol's expression must be a multiple of 6, i.e. 6x3, 12x3, 18x3, 24x3, 30x3 and so on. Hence, all possible expressions that could be Carol's are 1/6x3, 1/12x3, 1/18x3, 1/24x3, 1/30x3 and so on.
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The diagram shows a square ABCD with side length k cm. MDE is a sector of a circle, centre D. E lies on the diagonal, BD, of the square. M is the midpoint of AD. Find the percentage of the square that is shaded.
Answers
The sοlutiοn οf the given prοblem οf square cοmes οut tο be 0.84% is the shaded area.
What precisely is a square?A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.
Here,
We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.
A sectοr is equal tο (45/360)k²/2 = 0.125k²
Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:
=> BE² + DE² = BD²
=> BE² + k² = (k√2)²
=> BE² = 2k² - k²
=> BE = k√2
Therefοre, the triangle BDE's area is:
=> A(triangle) = (1/2)
=> BE*DE = (1/2)
=> (k√2)(k√2) = k²
Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:
=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²
Cοnsequently, the amοunt οf the rectangle that is shaded is:
=> percentage = (A(shaded) / A(square)) x 100%
=> ( 0.0084k² / k²) x 100%
=> 0.84%
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3) For a random sample of 100 American cities, it is found that there is a significant linear correlation between the number of robberies last year and the number of schools in the city. Does this suggest that building more schools in a city could lead to more robberies? (1 pt.) Why or why not? (2 pts.)
Answers
Building more schools could lead to more robberies.
what is sample space?
In probability theory, the sample space is the set of all possible outcomes of a random experiment or process. It is denoted by the symbol "S".
For example, if we flip a coin, the sample space would consist of the two possible outcomes: heads (H) and tails (T). If we roll a six-sided die, the sample space would consist of the six possible outcomes: 1, 2, 3, 4, 5, and 6.
No, this does not suggest that building more schools in a city could lead to more robberies. Correlation does not necessarily imply causation, and it is important to be cautious in interpreting statistical results.
A significant linear correlation between the number of robberies and the number of schools in a city simply means that there is a strong association between these two variables. It does not provide evidence of causation. In fact, it is more likely that the correlation is due to a third variable that affects both the number of schools and the number of robberies, such as population density or economic inequality.
Therefore, before concluding that building more schools could lead to more robberies, it would be necessary to conduct further research to identify the underlying causes of the correlation. Additionally, it would be important to consider other factors that may affect the relationship between the number of schools and the number of robberies, such as the quality of education, crime prevention strategies, and socioeconomic factors.
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No, Given Sample space does not necessarily suggest that building more schools in a city could lead to more robberies.
What exactly is a sample space?
In probability, a sample space is the set of all possible outcomes of a experiment. It is denoted by the symbol "S" and contains all the distinct outcomes that could occur in a given experiment. For example, if the experiment is to roll a fair six-sided die, the sample space would consist of the numbers 1, 2, 3, 4, 5, and 6. Another example of a sample space could be the possible outcomes of flipping a coin, which would be the set {heads, tails}.
Now,
No, this does not necessarily suggest that building more schools in a city could lead to more robberies.
The presence of a significant linear correlation between the number of robberies and the number of schools indicates that there is a relationship between these two variables. However, correlation does not imply causation. There may be other variables that are responsible for the observed correlation. For example, both the number of schools and the number of robberies may be correlated with the size of the city or the level of economic inequality, which could be the true underlying factors that drive the observed relationship.
Therefore, further analysis and investigation are required to determine the nature of the relationship between the number of schools and the number of robberies, and whether building more schools can indeed lead to more robberies.
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find the equation of a straight line passing through a point (-2, 1) and perpendicular to the line -3x +5y +2=0
Answers
Answer:
y= -5/3x - 7/3
Step-by-step explanation:
1. solve the line
-3x +5y + 2 = 0
+3x +3x
5y + 2 = +3x
-2 -2
5y = +3x - 2
/5 /5
y= 3/5x -2/5
2. find slope
perpendicular lines have an opposite reciprocal slope to original line so your slope is now -5/3
3. find b ( y - intercept )
point ( -2 , 1 )
y - y1 = m ( x - x1 )
y - 1 = -5/3 ( x + 2 )
y -1 = -5/3x - 10/3
+1 + 1
y= -5/3x - 7/3
Consider a multinomial distribution with 3 different outcomes, that is,
(Z1, Z2, Z3)∼ Multinomial(n,p1,p2,p3),p1+p2+p3=1. Derive the conditional distribution of Z2 given Z1=z1. That is, work out its pmf and name the distribution.
Answers
z3 = n − k − z1 − z2
A multinomial distribution with 3 different outcomes is given by (Z1, Z2, Z3)∼ Multinomial(n,p1,p2,p3), where p1 + p2 + p3 = 1. The conditional distribution of Z2 given Z1=z1 is to be derived. The pmf and distribution will be found.Let k be the number of trials with Z1 = z1. Therefore, the number of trials with Z2 = z2 is n − k. Then, the conditional distribution of Z2 given Z1=z1 is(Z1,Z2=n−k,Z3)∼Multinomial(k,p1,p2,p3)×Multinomial(n−k−1,p1′,p2′,p3′),where p1' = p1 / (1 − p1), p2' = p2 / (1 − p1), and p3' = p3 / (1 − p1).As a result, the pmf of the conditional distribution of Z2 given Z1=z1 is given byP(Z2 = z2 | Z1 = z1) = (k!/(z1!z2!(n−k−z1−z2)!))×(p1z1p2z2p3n−k−z1−z2)×(n−k−1)!/(z3!(n−k−z3−1)!(p1'z1+p2'z2+p3'z3)n−k−1), where z3 = n − k − z1 − z2. The distribution obtained is named a "conditional multinomial distribution".
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HELP ME!!
In the figure shown below, ab is a tangent to circle “O” at “a”. Also ab=16, and wb=12. Find the length of the radius.
Answers
It’s not that complicated! If u have any question, fell free to ask! :)
Under her cell phone plan, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Sydney can use while staying within her budget.
Answers
The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.
How to illustrate the information?
From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.
The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:
35.50 + 5x < 50
Collect like terms
5x < 50 - 35.50
5x < 14.50
x < 14.50 / 5
x < 2.9
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When eighteen is reduced by one-third of a number, the result is 9. Find the number.
Answers
Answer:
27
Step-by-step explanation:
aone third of 27 is 9, and 18 - 9 = 9
find an equation of a line with a slope of -1 and having the point (-2,-6) on the line
Answers
Answer: is there a pic?
Step-by-step explanation: is there a pic of what your working on?
Answer:
y=-x-8
Step-by-step explanation:
formular for finding an equation on a line is y-y1=m(x-x1) whiles m is the slope or gradient then x1 is -2 and y1 is -6 then you substitute to the formular you state down
I HAVE 5 MINS PLEASE HELPPPPPPPPP 30point
Answers
Never true;
The sum of two irrational numbers is irrational
Always true;
The sum of two rational numbers is rational
The product of two rational numbers is rational
Sometimes true;
The product of two irrational numbers is irrational
What are rational numbers?Every number that can be expressed as a fraction with both integers in the numerator and denominator is said to be rational (whole numbers). Numerator cannot be zero.
Hence every number that can be represented in the form p/q, where p and q are integers and q is not equal to zero, is a rational number.
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What is QS and what is c = to
Answers
The value of QS is 4.5c + 9.5.
What is parallelogram?A parallelogram is a four-sided plane figure with opposite sides parallel and equal in length. Its opposite angles are also equal.
Since Q is the midpoint of the diagonals RT and SU in parallelogram RSTU, we have:
QS = 1/2 RT ...(1)
QU = 1/2 SU ...(2)
Also, since RU||ST and RS||UT, we know that triangles QRU and QST are similar by AA similarity, so:
QR/QS = QU/QT
Substituting the given values and using (1) and (2), we get:
QR/(6c - 8) = (c + 7)/QT
Cross-multiplying and simplifying, we get:
QR = (6c - 8)(c + 7)/(2c - 1)
QR = (6c^2 + 34c - 56)/(2c - 1)
QR = 3(2c^2 + 11c - 18)/(2c - 1)
QR = 3(2c - 1)(c + 9)/(2c - 1)
QR = 3(c + 9)
Now, using (1), we have:
QS = 1/2 RT
QS = 1/2 (QR + RU)
QS = 1/2 (3(c + 9) + (6c - 8))
QS = 1/2 (9c + 19)
QS = 4.5c + 9.5
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Find the length of the diagonals of rectangle WXYZ. WY = 14x + 10; XZ = 11x + 22
Answers
The length of the diagonal of the rectangle is 66
How to find the diagonals of the rectangle?Here we have the rectangle WXYZ.
In that notation, we would have:
WX
XY
YZ
ZW
As the sides
And:
WY
XZ
as the diagonals.
We know that the values of the two diagonals must be the same ones, then we can write:
WY = XZ
14x + 10 = 11x + 22
Now we can solve that for x.
14x - 11x = 22 - 10
3x = 12
x = 12/3 = 4
then the length of the diagonal is:
WY = XZ = 14*4 + 10 = 66
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How many solutions does the nonlinear system of equations graphed below
have?
O A Zero
• B. One
O C. Four
O D. Two
Answers
Answer:
D. Two.
Step-by-step explanation:
The two graphs touch each other at two different points, meaning they have two solutions.
The equation of the passing through the points
(-1,-4) and (3,0)
Answers
The equation of the line passing through the points (-1, -4) and (3, 0) is y = x - 3.
To find the equation of the line passing through two points, we need to use the point-slope form of the equation of a line.
Point-slope form: y - y₁ = m(x - x₁)
where:
(x₁, y₁) is one of the given points on the line
m is the slope of the line
To find the slope of the line passing through (-1, -4) and (3, 0), we can use the formula:
m = (y₂ - y₁)/(x₂ - x₁)
where:
(x₁, y₁) = (-1, -4)
(x₂, y₂) = (3, 0)
m = (0 - (-4))/(3 - (-1))
m = 4/4
m = 1
Now we can use either of the two points and the slope to write the equation of the line.
Let's use point (-1, -4):
y - (-4) = 1(x - (-1))
y + 4 = x + 1
y = x - 3
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∠A and
∠
�
∠B are vertical angles. If m
∠
�
=
(
2
�
+
19
)
∘
∠A=(2x+19)
∘
and m
∠
�
=
(
3
�
−
18
)
∘
∠B=(3x−18)
∘
, then find the measure of
∠
�
∠A
Answers
If m ∠A=(2x+19)° and m ∠B=(3x−18)° of vertical angles ∠A and ∠B, the the measure of ∠A is 93° (degrees)
Vertical angles are formed when two lines intersect. They are opposite to each other and have the same measure. Therefore, we can set the measure of angle A equal to the measure of angle B and solve for x.
m ∠A = m ∠B
2x + 19 = 3x - 18 (Substitute the given measures of ∠A and ∠B)
19 + 18 = 3x - 2x (Add 2x to both sides and subtract 19 from both sides)
37 = x
Now that we have found the value of x, we can substitute it into the measure of ∠A to find its measure:
m ∠A = 2x + 19
m ∠A = 2(37) + 19 (Substitute x = 37)
m ∠A = 93
Therefore, the measure of ∠A is 93 degrees.
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Complete Question
∠A and ∠B are vertical angles. If m ∠A=(2x+19)° and m ∠B=(3x−18)°, then find the measure of ∠A
1. The graph shown is a graph of f'(x). If f(2)=5, use the graph to find f(8).
A. 16.5
C. 25.5
D. 21.5
E. 25
Answers
The value of f(8) is equal to D)21.5.
What is meant by area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
The graph of f'(x) is given in the figure.
We know that
[tex]\int\limits^a_b {f'(x)} \, dx =f(a)-f(b)[/tex].
Therefore since we have f(2) and we have to find f(8), we will take the area under the given graph from x=2 to 8
[tex]\int\limits^8_2 {f'(x)} \, dx =f(8)-f(2)\\\\2*3+2*3+\frac{1}{2}*3*3=f(8)-5\\ 16.5=f(8)-5\\f(8)=21.5[/tex].
Therefore f(8) is equal to D)21.5.
To learn more about the area under the graph, refer to the link below:
https://brainly.com/question/30211849
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What is 268.8 divided by 56 using division ASAP
Answers
Answer: 4.8
Step-by-step explanation: 268.8 divided by 56 is 4.8
TRIGONOMETRY
Grade 10 Math
Calculate to the nearest 0.1 degree, the size of alpha in the drawing above.
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Answers
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\tan(\alpha )=\cfrac{\stackrel{opposite}{5}}{\underset{adjacent}{4}}\implies \alpha=\tan^{-1}\left( \cfrac{5}{4} \right)\implies \alpha \approx 51.3^o[/tex]