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 degrees
17°17 degrees
6°6 degrees
84°
(1 point)
Responses
90°90 degrees
17°17 degrees
6°6 degrees
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 \(\theta\) can be calculated using the formula:
\[
\theta = \tan^{-1}\left(\frac{\text{height of the building}}{\text{length of shadow}}\right)
\]
In this scenario, the height of the building is 125 feet and the length of the shadow is 13 feet. Plugging in these values, we have:
\[
\theta = \tan^{-1}\left(\frac{125}{13}\right)
\]
Now, calculating the fraction:
\[
\frac{125}{13} \approx 9.6154
\]
Next, we find the angle using the arctan function:
\[
\theta \approx \tan^{-1}(9.6154)
\]
Now, using a calculator to find the inverse tangent:
\[
\theta \approx 82.7°
\]
Rounding off to the nearest degree, we get approximately 83°. However, based on the options provided, the closest one is:
**84°**
So the answer is:
**84°**
\[
\theta = \tan^{-1}\left(\frac{\text{height of the building}}{\text{length of shadow}}\right)
\]
In this scenario, the height of the building is 125 feet and the length of the shadow is 13 feet. Plugging in these values, we have:
\[
\theta = \tan^{-1}\left(\frac{125}{13}\right)
\]
Now, calculating the fraction:
\[
\frac{125}{13} \approx 9.6154
\]
Next, we find the angle using the arctan function:
\[
\theta \approx \tan^{-1}(9.6154)
\]
Now, using a calculator to find the inverse tangent:
\[
\theta \approx 82.7°
\]
Rounding off to the nearest degree, we get approximately 83°. However, based on the options provided, the closest one is:
**84°**
So the answer is:
**84°**