Answer:
The ratio of two sides of one right triangle is the same of the corresponding sides of any its similar triangles. ... Then a/b = A/B, which means that this ratio is a constant. The same for a/c = A/C, and b/c = B/C
Hope it helps
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Thank you
We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
Similar right triangles can be used to derive the definitions of trigonometric ratios, which are commonly abbreviated as sin, cos, and tan.
Consider a right triangle ABC, where angle A is the right angle.
Let's draw another right triangle ABD where angle A is also the right angle and angle B is congruent to angle D.
We say that triangles ABC and ABD are similar, which means that their corresponding angles are congruent and their corresponding sides are proportional.
Let's label the sides of triangle ABC as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side b.
The side opposite angle C is side c.
We can label the sides of triangle ABD as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle D is side y.
Since triangles ABC and ABD are similar, we can write the following proportion:
b / a = x / y
Solving for b, we get:
b = (x / y) * a
Now, we can use the Pythagorean theorem to relate the sides of triangle ABC:
a² = b² + c²
Substituting b with its value, we get:
a² = ((x / y) a)² + c²
Simplifying, we get:
a² = (x² / y²) a² + c²
Multiplying both sides by y², we get:
a² x y² = x² a² + c² y²
Now, we can solve for x/y, which is equal to sin(B) and y/a, which is equal to cos(B):
sin(B) = x / y = sqrt(a^2 - c^2) / a
cos(B) = y / a = c / a
Similarly, we can consider another triangle ABE, where angle A is the right angle and angle B is congruent to angle E.
We say that triangles ABC and ABE are also similar.
Let's label the sides of the triangle ABE as follows:
The side opposite angle A is side a (the hypotenuse).
The side opposite angle B is side x.
The side opposite angle E is side z.
Using the Pythagorean theorem for triangle ABC, we get:
a² = b² + c²
Substituting b with its value from triangle ABE, we get:
a² = ((z / x) a)² + c²
Simplifying, we get:
a² = (z² / x²) x a² + c²
Multiplying both sides by x², we get:
a² x² = z² a² + c² x²
Now, we can solve for z/x, which is equal to tan(B):
tan(B) = z / x = √(a² - c²) / c
Therefore,
We have derived the definitions of the three basic trigonometric ratios sin, cos, and tan using similar right triangles.
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Which number is in the solution set of this equation? 7x − 9 = 40
Answer: the answer is 7
Step-by-step explanation: add 9 to both sides, eliminating -9 so now you have 7x=49 divide both by 7 and you get x= 7 check it by inputing 7 for x, 7(7)-9=40
7(7)=49 next 49-9= 40
it checks out, so x= 7
The perimeter of a rectangle is 36 meters. If the length of the rectangle is 10 meters, what is the width (in meters)?
What is the measure of n?
6
24
n
m
n =
[?]
Answer:
n = 12
Step-by-step explanation:
By applying geometric mean theorem in the given right angle triangle,
[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]
BD² = AD × DC
Now substitute the values of each side given,
n² = 6 × 24
n² = 144
n = 12
A baseball player gets a hit 20% of the times he is at bat. Out of the next 15 times at bat, how many hits can you expect the player to get?
Answer:
...
Step-by-step explanation:
The batsman will hit =20% of 15
= 15/5
= 3
Answer:
3
Step-by-step explanation:
15 x 0.20
Wanna be the Brainiest
Answer:
156cm^3
Step-by-step explanation:
V= 1/2 a*c*h
a=3
c=8
h=13
3*8*13=312
312/2=156
increase £196 by 9%
old old working out need asap
Answer:
£213.64
Step-by-step explanation:
You do 196(0.09)
That's 17.64
The you add the two
196+17.64
The way I got 9 was from 9%.
To make it in decimal form you have to move the decimal over two places.
Hope this helps
i need help ASAP please
Answer:
umm so i belive you will mulltiply all of thoes together
Step-by-step explanation:
chicken nuggies are good :0
Answer:
number 3
Step-by-step explanation:
p represents amount of tickets sold at the pre-sale and d represents the amount of tickets sold at the door. If you add p + d, that equals the total amount of tickets sold which is 345 tickets.
So:
p + d = 345
Pre-sale tickets (p) cost $7 while tickets at the door (d) cost $10, and the total amount of money mad is $2550.
So:
7p + 10d = 2550
Answer should be the equations in number 3.
Select the two values of x that are roots of this equation.
2x-5=-3x2
Answer:
Step-by-step explanation:
I need help with fractions
Answer: 3 1/2 represents G and 2 3/4 represents point K
Step-by-step explanation: If you look at the first on it is 3 1/2 because it is in the middle and the second one is divided in fourths so K is 2 3/4.
consider the image that shows a tower anchored by a guy with the guy wire is attached at point b on the tower 119 feet above the ground and then anchored to the ground at point a 120 feet from the base of the tower.
Options are: A) sin0= 119/120, B) sin0= 120/119, C) sin0= 119/169, and D) sin0= 120/169
Answer:
Step-by-step explanation:
[tex]sin\theta=\frac{opposite}{hypotenuse}\\ \\ sin\theta=\frac{119}{169}\ (answer\ C)[/tex]
The equation y=250,000(1.1)x closely models the value of his home, y, when x is the number of years since 2002.
Using this equation, what would we have expected to be the value of his condo in the year 2006?
Value in 2006:
Answer:
The value in 2006 is 366,025
Step-by-step explanation:
Here, we want to get the value of y in 2006
what we have to do here is to find and substitute the missing value of x
The missing value x is the difference between the number of years in 2002 and 2006
we have this as 2006-2002 = 4
so we have to substitute 4 here for x
Thus, we have this as;
y = 250,000(1.1)^4
y = 366,025
Help Me, Now! B. What is the value of each funtion at x = 1?
Answer:
Step-by-step explanation:
Use the course calculator to solve this problem:
8 + 17 × 26
Answer:
450
Step-by-step explanation:
8+17=25
25x26=450
Answer: 500
Step-by-step explanation:
You have to do multiplication first according to PEMDAS so you do 17 times 26 and you get 442 add 8 you get 500.
A rectangle has a perimeter of 18. The height of the rectangle is 4 cm. What is the area of the rectangle?
Answer:
20
Step-by-step explanation:
Perimeter of rectangle= 2l+2h so 2l+2(4)=18. SO 2l=10. l=5
Area=bh
(5)(4)=20cm
Which graph represents the solution set of - 4x - y <- 6?
Answer: it’s D
Step-by-step explanation:
The Linear Inequality - 4x - y <- 6 represents option d, of the solution set.
What is Linear Inequality?
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both. Examples of numerical inequality include 1011 and 20>17, whereas algebraic inequalities include x>y, y19-x, and x z > 11 (also called literal inequalities). The mathematical equation when both sides are not equal is called an inequality. Inequality occurs when a connection compares two expressions or two numbers in an unequal manner. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the phrase. Polynomial inequality, rational inequality, and absolute value inequality are the many sorts of inequalities. The symbols "and ">" signify tight inequalities, whereas " and "signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
In the given question, we have given the graph of the inequality 4x - y <- 6, So, we need to find the best suitable graph that represents the graph of the given Inequality.
So, the Inequality is:
- 4x - y <- 6.
So, we can substitute the value of x and y;
So, substitute x = 1;
So, The y value will be less than 2;
That is:
y < 2;
Again let's put the value of x = -1;
we get the value of y as less than 10.
y<10;
So, by substituting the values as mentioned we can see that the value of y is decreasing.
So, by plotting the values in the graph, we can get the correct graph.
Hence, The correct answer is option d.
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what is 6x7 i give brainlest
Answer:
42
Step-by-step explanation:
The product of 6 multiplied by 7 is 42.
We have to find the value of 6×7.
To find the product of 6 multiplied by 7, you simply multiply the two numbers together.
6 multiplied by 7 can be calculated as:
6 x 7
When six is multiplied with seven we get forty two.
= 42
Therefore, the product of 6 multiplied by 7 is 42.
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What is an equation of the line that is parallel to y=-5x+6 and passed through the point (-4,-1)
Answer:y=-5x-21
Step-by-step explanation:\
y=mx+b
-1=-5(-4)+b
-1=20+b Subtract 20 from each side
-21=b
The equation is y=-5x-21
In your own words, explain the steps you would need to take to find a slope from data in a table.
Answer:
Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Step-by-step explanation:
Answer:
To Find the slope of a data table, you first need to plot two points on the line. It is easiest if the points are on a coordinate with whole numbers (i.e. (3,6 and (4,8)). Once you have plotted two pints, you then need to take the value of the point with the largest x value, and subtract the other points from it (i.e. (4,8)-(3,6)=(1,2). Then, take the new y value, and divide it by the new y-value (i.e. (2/1), and you have your slope.
Step-by-step explanation:
plot points (3,6), (4,8)
subtract points (4,8)-(3,6)=(1,2)
divide new points 2/1
m=2/1, or 2
A) complementary
B) Alternate exterior
C) alternate interior
D) corresponding
Answer:
C
Step-by-step explanation:
Its inside
39/8 as a decimal... I've forgotten how to turn fractions into decimals
Answer:
4.222222 or jus 4.2 with - over the 2 to indicate multiple 2's
Answer:
4.875
Step-by-step explanation:
Pretty simple, just divide the numerator by the denominator.
is 17/5 rational or irrational
Answer:
rational
Step-by-step explanation:
Answer:
rational
Step-by-step explanation:
16. What are the missing sides?
TE
4 cm
3 cm
?
?
5 cm
10 cm
Determine if two triangles are congruent. If they are, state how you know.
A: SSS
B: SAS
C: HL
D: AAS
help me ASAP please!
Answer:
They are congruent. SSS
Step-by-step explanation:
All the sides are the same, clearly stated by the signs on the borders.
What does 2x-9=7x-44
Answer:
Isolate the variable by dividing each side by factors that doesn't contain the variable.
Exact form: x = 154/9
Decimal form: x = 17.1
Mixed number form: x = 17 1/9
Step-by-step explanation:
hope that helps...
have a good day
How do I know that these are not a function?
0,-1
2,3
0,4
2,5
0,6
2,7
Answer:
there are multiple 0's in the same area, and multiple 2's.
Step-by-step explanation:
Paul is growing a rectangular rose garden. His area is 5x2+ 8x +3. What are the dimensions of his rectangle?
Answer:
[tex]Length = 5x + 3[/tex]
[tex]Width = x +1[/tex]
Step-by-step explanation:
Given
[tex]Area = 5x^2 + 8x + 3[/tex]
Required
Determine the dimensions
To do this, we simply factorize the given expression.
[tex]Area = 5x^2 + 8x + 3[/tex]
Expand
[tex]Area = 5x^2 + 5x +3x+ 3[/tex]
Factorize
[tex]Area = 5x(x + 1) +3(x+ 1)[/tex]
Factor out x + 1
[tex]Area = (5x +3) (x+ 1)[/tex]
Area is calculated as:
[tex]Area = Length * Width[/tex]
So:
[tex]Length = 5x + 3[/tex]
[tex]Width = x +1[/tex]
What will be the first negative term in the sequence 87,84,81
Answer:
a₃₁
Step-by-step explanation:
The terms have a common difference between consecutive terms, that is
d = 84 - 87 = 81 - 84 = - 3
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 87 and d = - 3 , then
[tex]a_{n}[/tex] = 87 - 3(n - 1) = 87 - 3n + 3 = 90 - 3n
To find when [tex]a_{n}[/tex] < 0 , solve
90 - 3n < 0 ( subtract 90 from both sides )
- 3n < - 90
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity, then
n > 30
Thus the 31st term will be the first negative term
Use the relationship between quantities to calculate the
missing values in the table.
A =
B = please help me
Answer:
A=750
B=1250
Step-by-step explanation: I got it right on edge.
Someone helppppp plsss j suck at math. ( pls answer only if your sure ur right)
Answer:
Step-by-step explanation:
PLS HELP 10 POINTS
QUESTION IN PIC
Answer:
Some integers are irrational
Step-by-step explanation:
An integer must be a whole number so it will always be rational.