Question
If a tree has a height of 126 feet, what would be the angle of elevation from level ground measured from 79 feet away? Round your answer to the nearest tenth of a degree.is the answer 57.0?
Answers
GPT-4o mini
To find the angle of elevation, we can use the tangent function in trigonometry. The angle of elevation \( \theta \) can be found using the following formula:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
In this case, the height of the tree (the opposite side) is 126 feet, and the distance from the tree (the adjacent side) is 79 feet.
So we have:
\[
\tan(\theta) = \frac{126}{79}
\]
Now, calculate \( \frac{126}{79} \):
\[
\frac{126}{79} \approx 1.595
\]
Next, we need to find \( \theta \) by taking the arctangent (inverse tangent) of \( 1.595 \):
\[
\theta \approx \tan^{-1}(1.595)
\]
Using a calculator, we find:
\[
\theta \approx 57.0^\circ
\]
So your answer of 57.0 degrees is correct, rounded to the nearest tenth of a degree.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
In this case, the height of the tree (the opposite side) is 126 feet, and the distance from the tree (the adjacent side) is 79 feet.
So we have:
\[
\tan(\theta) = \frac{126}{79}
\]
Now, calculate \( \frac{126}{79} \):
\[
\frac{126}{79} \approx 1.595
\]
Next, we need to find \( \theta \) by taking the arctangent (inverse tangent) of \( 1.595 \):
\[
\theta \approx \tan^{-1}(1.595)
\]
Using a calculator, we find:
\[
\theta \approx 57.0^\circ
\]
So your answer of 57.0 degrees is correct, rounded to the nearest tenth of a degree.