Question
A man is looking up at a building and wants to measure the angle from where he is to the top of the building. Find the angle measure.
0
55 m
A
20 m
(1 point)
Responses
45
45
90
90
30.6
30.6
70.0
0
55 m
A
20 m
(1 point)
Responses
45
45
90
90
30.6
30.6
70.0
Answers
GPT-4o mini
To find the angle measure from the man to the top of the building, we can use trigonometry. The problem likely uses the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle.
In this case, the height of the building (20 m) would be the "opposite" side and the distance from the man to the base of the building (55 m) would be the "adjacent" side.
We can use the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{55}
\]
Now we can calculate the angle \(\theta\):
1. Calculate \(\frac{20}{55}\):
\[
\frac{20}{55} \approx 0.3636
\]
2. Now take the arctangent of that value:
\[
\theta = \tan^{-1}(0.3636)
\]
Using a calculator:
\[
\theta \approx 20.0^\circ
\]
Therefore, the angle measure is approximately \(20^\circ\).
Based on the options provided, the best match is:
**20 m**
In this case, the height of the building (20 m) would be the "opposite" side and the distance from the man to the base of the building (55 m) would be the "adjacent" side.
We can use the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{20}{55}
\]
Now we can calculate the angle \(\theta\):
1. Calculate \(\frac{20}{55}\):
\[
\frac{20}{55} \approx 0.3636
\]
2. Now take the arctangent of that value:
\[
\theta = \tan^{-1}(0.3636)
\]
Using a calculator:
\[
\theta \approx 20.0^\circ
\]
Therefore, the angle measure is approximately \(20^\circ\).
Based on the options provided, the best match is:
**20 m**