While standing at the left corner of the schoolyard in front of her school, Suzie estimates that the front face is 8.9 m wide, and 4.7 m high. From her position, Suzie is 12.0 m from the base of the right exterior wall. She determines that the left and right exterior walls appear to be 39 degrees apart. From her position, what is the angle of elevation, to the nearest degree, to the top of the left exterior wall.
46
use 8.8^2 = x^2 + 12^2 - 2(12)(x)(cos37)
To find the angle of elevation to the top of the left exterior wall, we can use the tangent function.
Step 1: Calculate the distance from Suzie's position to the top of the left exterior wall.
To find this distance, we can use the width and height of the front face of the schoolyard. We can use the Pythagorean theorem because we have a right triangle formed by Suzie's position, the base of the left exterior wall, and the top of the left exterior wall.
Using the Pythagorean theorem:
Distance^2 = (Distance to base of left exterior wall)^2 + (Height of front face)^2
Distance^2 = (12.0 m)^2 + (4.7 m)^2
Distance^2 = 144 + 22.09
Distance^2 = 166.09
Distance = √166.09
Distance = 12.9 m (approximately)
Step 2: Calculate the opposite side of the triangle.
The opposite side of the triangle is the height of the front face of the schoolyard.
Opposite side = Height of front face = 4.7 m
Step 3: Calculate the tangent of the angle of elevation.
Tangent(angle of elevation) = Opposite side / Adjacent side
Tangent(angle of elevation) = 4.7 m / 12.9 m
Tangent(angle of elevation) = 0.364341 (approximately)
Step 4: Find the angle of elevation.
Using the inverse tangent function, we can find the angle of elevation.
Angle of elevation = arctan(0.364341)
Angle of elevation = 20.6 degrees (approximately)
Therefore, the angle of elevation, to the nearest degree, to the top of the left exterior wall is 21 degrees.
To find the angle of elevation to the top of the left exterior wall, we need to use trigonometry. Specifically, we can use the tangent function.
First, let's sketch out the scenario to visualize it better:
```
|\
| \
| \
Suzie's Position| \ Left Exterior Wall
| \
| \
| \
Ground | \
| \
|________\
Base of Right Exterior Wall
```
Now, if we draw a right triangle from Suzie's position to the top of the left exterior wall, we can use trigonometry to find the angle of elevation.
Let's call the angle of elevation (the angle between the horizontal ground and Suzie's line of sight to the top of the left exterior wall) as angle A.
We know that the opposite side (the height of the left exterior wall) is 4.7 m, and the adjacent side (the distance from Suzie's position to the left exterior wall) is 8.9 m.
Using the tangent function:
tan(A) = opposite/adjacent
tan(A) = 4.7/8.9
Now, we can use a calculator to find the value of A:
A ≈ arctan(4.7/8.9)
Using a calculator, we find:
A ≈ 28.78 degrees
Therefore, the angle of elevation from Suzie's position to the top of the left exterior wall is approximately 28.78 degrees, to the nearest degree.