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
90°
90°
6°
6°
17°
17°
84°
Responses
90°
90°
6°
6°
17°
17°
84°
Answers
GPT-4o mini
To find the angle of elevation from the end of the shadow to the top of the building, we can use the inverse tangent (arctan) function. The angle of elevation is calculated as follows:
\[
\text{angle} = \tan^{-1}\left(\frac{\text{height of the building}}{\text{length of the shadow}}\right)
\]
Given the height of the building is 125 feet and the length of the shadow is 13 feet, we can substitute the values:
\[
\text{angle} = \tan^{-1}\left(\frac{125}{13}\right)
\]
Calculating that:
\[
\frac{125}{13} \approx 9.615384615384615
\]
Now, we need to find the arctan of that value:
\[
\text{angle} \approx \tan^{-1}(9.615384615384615)
\]
Using a calculator to find the arctangent:
\[
\text{angle} \approx 84°
\]
Thus, the approximate angle of elevation from the end of the shadow to the top of the building is **84°**.
\[
\text{angle} = \tan^{-1}\left(\frac{\text{height of the building}}{\text{length of the shadow}}\right)
\]
Given the height of the building is 125 feet and the length of the shadow is 13 feet, we can substitute the values:
\[
\text{angle} = \tan^{-1}\left(\frac{125}{13}\right)
\]
Calculating that:
\[
\frac{125}{13} \approx 9.615384615384615
\]
Now, we need to find the arctan of that value:
\[
\text{angle} \approx \tan^{-1}(9.615384615384615)
\]
Using a calculator to find the arctangent:
\[
\text{angle} \approx 84°
\]
Thus, the approximate angle of elevation from the end of the shadow to the top of the building is **84°**.