9. A building 62 feet tall casts a shadow 21 meters long. At what angle is the sun shining on the building?
A. 19.80
B. 18.71
C. 70.20
D. 71.29
Answers
First, we imagine a right triangle. Second, we are given that the building is 62 feet tall. Since the height of building is vertical straight - that means the height is opposite side of triangle. It also casts a shadow 21 meters long. Shadow should be the adjacent side because it casts on the ground and not on the air.
If we imagine the right triangle + the problem in our head, we'd get the triangle that the opposite side is 62 feet tall and the adjacent side is 21 meters long.
Use the tangent ratio to find the angle of sun shining.
[tex] \large \boxed{ \tan \theta = \frac{opposite}{adjacent} }[/tex]
Substitute adjacent = 21 and opposite = 62 in the ratio.
[tex] \large{tan \theta = \frac{62}{21} }[/tex]
For this part, you might need a calculator or trigonometric table because some values cannot be exactly found.
From the equation, we should get 71.288 which we round the answer to nearest hundreth and the answer would be 71.29
Answer
The answer is 71.29Answer:
71.29°
Step-by-step explanation:
By question its given that , a 62 feet tall tree cast a shadow of 21 m long. We need to find the angle at which the sun is shining on the building .
For this we gonna imagine a right angle triangle . Where , the length of the shadow will be the base of the triangle and the height of the building will be the perpendicular on the triangle .
Here since we have got perpendicular and base , we can use the ratio of tan . We know that tan is defined as perpendicular by base , that is ,
[tex]\implies tan \theta =\dfrac{perpendicular}{base}[/tex]
where theta is the angle between the Ray of the the sun and the the shadow of the building.Plug in the respective values , we have ,
[tex]\implies tan \theta =\dfrac{62}{21} \\\\\implies\theta = tan^{-1}\bigg( \dfrac{62}{21}\bigg) \\\\\implies \underline{\underline{\theta = 71.29^o }}[/tex]
Hence the required answer is 71.29° .
Related Questions
If line ab is tangent to circle c , find AC?
Can anyone help?
Answers
Answer:
Step-by-step explanation:
If AB is tangent to the circle, the AB makes a right angle with the radius BC. That means that triangle ABC is a right triangle and we need Pythagorean's Theorem to find the missing side which is the hypotenuse.
[tex]AC^2=AB^2+BC^2[/tex] and filling in:
[tex]AC^2=14^2+9^2[/tex] and
[tex]AC^2=196+81[/tex] and
[tex]AC^2=277[/tex] so
[tex]AC=\sqrt{277}[/tex] ≈ 16.64
AC = 16.64
The Tangent theorem
"It states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency."
From given diagram,
tangent AB = 14 units
radius BC = 9 units
Using tangent theorem,
AB is perpendicular to BC.
This means ΔABC is right triangle with ∠B = 90°
Using Pythagoras theorem,
[tex]AC^2=AB^2+BC^2[/tex]
⇒ [tex]AC^2=14^{2}+9^{2}[/tex]
⇒ [tex]AC^2=196+81[/tex]
⇒ [tex]AC^2=277[/tex]
⇒ [tex]AC=\sqrt{277}[/tex]
⇒ [tex]AC=16.64[/tex]
Therefore, AC = 16.64
Learn more about tangent to the circle here:
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Which is the rationalized form of the expression. A, B , C, or D?
Answers
Answer:
C
Step-by-step explanation:
Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.
You get answer C.
Convert r=53sinθ−cosθ to rectangular form.
Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.
Answers
Answer:
[tex]y = \frac{1}{3} x + \frac{5}{3}[/tex]
Step-by-step explanation:
r = 5/(3sinθ-cosθ)
multiply both sides by (3sinθ-cosθ):
r(3sinθ-cosθ) = 5
expand:
3rsinθ-rcosθ = 5
replace rsinθ with y and rcosθ with x:
3y-x = 5
add x to both sides:
3y = x + 5
divide both sides by 3:
y = 1/3x + 5/3
: )
I don't understand math...i probably never will
Answers
Answer:
1/2 9/8
17/12 23/30
81/70 2/3
Step-by-step explanation:
I ordered it the way it appears in the image.
What is the slope of the graph of 3x - 7y = 10 *
3/7
O-37
O 3
O -7
Answers
Answer:
Step-by-step explanation:
Solve this for y to determine the slope. Solving for y gets our line into the slope-intercept form, y = mx + b, where the number value of m will be the slope.
-7y = -3x + 10 and
[tex]y=\frac{-3}{-7}x+\frac{10}{-7}[/tex] which simplifies down to
[tex]y=\frac{3}{7}x-\frac{10}{7}[/tex]
The value for m is 3/7 so that is the slope, the first choice given.
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth
A. 5
B. 5.8
C. 17.3
D. 8.7
Answers
Answer:
B) 5.8
Step-by-step explanation:
Are these correct?
Histograms/Leaf & Stem plot
Answers
Answer:
yes that's correct :)
Step-by-step explanation:
Please help ;-; hdsjvhskjvbsjhvlsjvh
Answers
Answer:
a)
10 markers : 7 USD
24 markers : 14 USD
42 markers : 21 USD
b)
64 markers : 28 USD
Step-by-step explanation:
10 markers : 7 USD
24 markers : 14 USD
For 10 markers, the price is 7 USD;
For 14 additional markers, the price increased by 7 USD;
Following the pattern, an additional 18 markers would see the price further increase by 7 USD;
So:
24 + 18 = 42
42 markers : 21 USD
Then, an additional 22 markers would cost 7 USD more than this;
42 + 22 = 64
64 markers : 28 USD
Calculate cos0 to two decimal places. 7 8 Xà A. 0.69 B. -0.14 C. -0.42 OD. -0.07
Correct answer: -0.07
Answers
Answer:
D. -0.07 to nearest hundredth.
Step-by-step explanation:
Applying the Cosine Rule:
11^2 = 7^2 + 8^2 - 2*7*8 cos O
cos O = (11^2 - 7^2 - 8^2) / (-2*7*8)
= 8/-112
= -0.07143.
what is the area pls
Answers
Answer:
125 i think
Step-by-step explanation:
Multiply 4x4=8 from the square then multiply 13 x 9= 117 then add 8+117 you will get 125
How can you apply the concept of area and perimeter in your everyday life?
Answers
PLEASE HELP SHOULD BE EASY!! WILL GIVE BRAINLIEST
Answers
.........................
Answer:
I believe the answer will be 6. Here's why.:
Step-by-step explanation:
The total volume of the rectangle is 24 inches. 4in x 6in= 24 in. Then there is a half semi-circle. So 24/2=12. The circle is called a circumference and since there is a half, that is called a diameter. I am not sure if my reasoing is correct, but I gave it try.
Which is the best explanation for why − √ 10 is irrational?
Answers
Step-by-step explanation:
- square root of 10 is irrational because it is less than zero. - square root of 10 is irrational because it is not a whole number.
Upon prime factorizing 10 i.e. 21 × 51, 2 is in odd power. Therefore, the square root of 10 is irrational.
Aimee says Bella is lying. Bella says Marc is lying. Marc says Bella is lying. Terry says Aimee is lying. How
many of the four children are lying?
a) 0 b)1 c)2 d)3 e)4
Answers
what is x in the equation 3x+4=2x+6?
Answers
Answer:
x= 2
Step-by-step explanation:
Answer:
3x + 4 = 2x + 6
3x +4 - 2x - 6 =0
x - 2 = 0
x = 2
3(2) +4 = 2(2) + 6
6 + 4 = 4 + 6
10 = 10
3x+2=2x+6
subtracting 2 from both sides
3x+2-2=2x+6-2
3x=2x+4
subtracting 2x from both sides
3x-2x=2x-2x+4
x=4
Bab in need of help!
Answers
Answer:
Third option is the correct answer
Step-by-step explanation:
Given end points are: [tex] (x_1, \:y_1) \:\&\: (x_2, \:y_2)[/tex]
[tex] \huge\purple {\therefore Midpoint =\bigg(\frac{x_1+x_2}{2},\: \frac{y_1+y_2}{2}\bigg)} [/tex]
is -49 a rational number? please explain
Answers
Go step by step to reduce the radical. 112
Answers
Answer:
4 sqrt(7)
Step-by-step explanation:
sqrt(112)
We know sqrt(a*b) = sqrt(a) sqrt(b)
Look for perfect squares
sqrt(16*7)
sqrt(16)sqrt(7)
4 sqrt(7)
Answer:
4√7
Step-by-step explanation:
√112
we know that ( a × b) = √a √ b
[tex] \small \sf \: \sqrt{16 \times 7} [/tex]
√16 × √7
4√7
plz help asap. i beg
Answers
The answer is -15.
Because others are rational numbers but not integers.
-15 is the only rational number and integer.
y-6=4(x+5) what is y and x intercept?
Answers
Answer:
x = [tex](-\frac{13}{2} ,0)[/tex] y = (0,26)
Step-by-step explanation:
First find the x intercept
To find the x intercept, substitute 0 for y and solve for x.
[tex](0)-6=4(x+5)[/tex]
Rewrite the equation as [tex]4(x+5)=(0)-6[/tex]
[tex]4(x+5)=(0)-6[/tex]
Subtract 6 from 0.
[tex]4(x+5)=-6[/tex]
Divide each term in [tex]4(x+5)=-6[/tex] by 4.
[tex]\frac{4(x+5)}{4} =\frac{-6}{4}[/tex]
Cancel the common factor of 4.
[tex]x+5=\frac{-6}{4}[/tex]
Simplify [tex]\frac{-6}{4}[/tex]
[tex]x+5=-\frac{3}{2}[/tex]
Subtract 5 from both sides of the equation.
[tex]x=-\frac{3}{2} -5[/tex]
To write [tex]-5[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex]
[tex]x=-\frac{3}{2}-5[/tex] · [tex]\frac{2}{2}[/tex]
Combine [tex]-5[/tex] and [tex]\frac{2}{2}[/tex].
[tex]x=-\frac{3}{2} +\frac{-5*2}{2}[/tex]
Combine the numerators over the common denominator.
[tex]x=\frac{-3-5*2}{2}[/tex]
Simplify the numerator.
[tex]x=\frac{-13}{2}[/tex]
Move the negative in front of the fraction.
[tex]x=-\frac{13}{2}[/tex]
x = [tex](-\frac{13}{2} ,0)[/tex]
-----------------------------------------------------------------------------------------------------
Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
[tex]y-6=4((0)+5)[/tex]
Add 0 and 5.
[tex]y-6=4 *5[/tex]
Multiply 4 by 5.
[tex]y-6=20[/tex]
Add 6 to both sides of the equation.
[tex]y=20+6[/tex]
Add 20 and 6.
[tex]y=26[/tex]
y = (0, 26)
Point F is reflected over the yaxis to create F. Use an ordered pair to name the location of F, and determine the
distance between Fand F.
Answers
Answer:
Reflection about the y-axis is according to the rule
(x,y)->(-x,y)
Therefore F(x,y) -> F'(-x,y)
The distance between F' and F is (-x,y)-(x,y)=-2x, or the positive distance is 2x.
also consider marking as Brainliest if this helped :)!!
3( x - 2 ) + 2 (4x - 1)
Answers
Answer:
11x-8
Step-by-step explanation:
First distribute the 3 and 2. (Only in the parenthesis!):
3(x-2)+2(4x-1)
3x-6+8x-2
Combine like terms:
3x+8x=11x
-6-2=-8
So the answer is:
11x-8
Compare and contrast angular momentum and linear momentum. Include two ways that they are alike and two ways that they are different. Be sure to discuss how mass affects both angular and linear momentum. (5 points)
Answers
Answer:
Linear momentum of an object is the product of the object’s mass and velocity. Linear momentum is a vector quantity, and the direction of momentum is taken to be the direction of the object’s velocity.
or an object with mass moving at a velocity , the angular momentum with respect to a reference point is defined using the cross product as:
where is the position vector of the object that describes the object’s position with respect to the reference point. The units for measuring angular momentum is kg m2 s-1. Since angular momentum is defined in terms of a cross product, the direction of the angular momentum vector is taken to be in a direction perpendicular to both the particle’s position vector and its velocity vector
Step-by-step explanation:
answer please need belp ???
Answers
180-161=19
So angle 1 is 19 degrees
What are the dimentions of an advertized 21 inch monitor with 4:3 ratio?
Answers
Answer:
13.75 inches and 15.87 inches
Step-by-step explanation:
split the ratio
1. Jimmy is selling tacos for $2 and enchiladas for $5. His total sales on were $235 and his total items sold was 65. (2pts) a. Create an equation that involves the total sales and the individual prices for the delicious items. b. Create an equation that relates the total items sold at his restaurant
Answers
Answer:
2x+5y=235 2x+5y=65
Step-by-step explanation:
Use the picture to solve for angle y
D
Z
х
116
y
A
С
B
64
ООО
32
16
Answers
9514 1404 393
Answer:
y = 32°
Step-by-step explanation:
Angle y is one of two congruent base angles in the isosceles triangle BCD that has angle B as its third angle:
2y + 116° = 180° . . . . . . . sum of angles in a triangle
y + 58° = 90° . . . . . . . . divide by 2
y = 32° . . . . . . . . . . . . subtract 58°
_____
To those of you copying this answer: the question here asks for angle y. The other variables can be found from ...
x = 2y = 64° . . . . . . . the arc is twice the measure of the inscribed angle
z = ∠CBD = 116°
Is this polynomial positive or negative?
Answers
Answer:
The polynomial is positive.
Given the box plot, will the mean or the median provide a better description of the center
Answers
Diane must choose a number between 61 and 107 that is a multiple of 4,7, and 14 . Write all the numbers that she could choose.
Answers
Answer:
84
Step-by-step explanation:
only three number are a multiple of 14
14 * 5 = 70
14 * 6 = 84
14 * 7 = 98
neither 70 nor 98 is a multiple of 4
only 84 is a multiple of 4, 7 and 14