Question

You are standing 23 feet from a building that is 55 ft tall. What is the angle of elevation from where you are standing to the top of the building? Solve for x, the degree of the elevation angle to the nearest tenth.
Sun
55 ft
Angle of
elevation
X
23 ft
(1 point)
Responses

x = 76.3
x = 76.3

x = 49.2
x = 49.2

x = 67.3
x = 67.3
x = 20.0

Answer 1

To find the angle of elevation \( x \) from where you are standing to the top of the building, we can use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building).

Given:
- Height of the building (opposite side) = 55 ft
- Distance from the building (adjacent side) = 23 ft

The formula involves the tangent of the angle:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{55}{23}
\]

Now, we calculate this fraction:
\[
\tan(x) = \frac{55}{23} \approx 2.3913
\]

Now, we need to find the angle \( x \) by taking the arctangent (inverse tangent) of that value:
\[
x = \tan^{-1}(2.3913)
\]

Using a calculator:
\[
x \approx 67.3^\circ
\]

So, to the nearest tenth of a degree, the angle of elevation \( x \) is approximately:
\[
\boxed{67.3}
\]