Question

A building casts a shadow. The building is 125 feet tall and the shadow is 13 feet in length from the base of the building. Using the inverse of tangent, what is the approximate angle of elevation from the end of the shadow’s length to the top of the building?(1 point)
Responses

6°
6°

17°
17°

84°
84°

90°

Answer 1

To find the angle of elevation from the end of the shadow to the top of the building, you can use the tangent function. The formula is:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this scenario:
- The height of the building (opposite side) is 125 feet.
- The length of the shadow (adjacent side) is 13 feet.

We need to find the angle \(\theta\):

\[
\tan(\theta) = \frac{125}{13}
\]

Now, we can calculate \(\theta\) by taking the inverse tangent (arctan) of the ratio:

\[
\theta = \tan^{-1}\left(\frac{125}{13}\right)
\]

Calculating the value:

\[
\frac{125}{13} \approx 9.6154
\]

Now find the angle:

\[
\theta \approx \tan^{-1}(9.6154)
\]

Using a calculator:

\[
\theta \approx 84.29°
\]

Rounding it gives approximately \( 84° \).

Therefore, the approximate angle of elevation is:

**84°**