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 57.7?
Answers
GPT-4o mini
To find the angle of elevation from level ground to the top of a tree, you can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case:
- The height of the tree (opposite side) = 126 feet
- The distance from the tree (adjacent side) = 79 feet
The tangent of the angle of elevation (\( \theta \)) can be calculated as:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{126}{79}
\]
Now, to find the angle \( \theta \), take the arctangent (inverse tangent) of the ratio:
\[
\theta = \tan^{-1}\left(\frac{126}{79}\right)
\]
Using a calculator to find this:
1. First, calculate the ratio:
\[
\frac{126}{79} \approx 1.5912
\]
2. Now, find the arctangent:
\[
\theta \approx \tan^{-1}(1.5912) \approx 57.7^\circ
\]
So, yes, you are correct that the angle of elevation is approximately \( 57.7^\circ \) when rounded to the nearest tenth of a degree.
In this case:
- The height of the tree (opposite side) = 126 feet
- The distance from the tree (adjacent side) = 79 feet
The tangent of the angle of elevation (\( \theta \)) can be calculated as:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{126}{79}
\]
Now, to find the angle \( \theta \), take the arctangent (inverse tangent) of the ratio:
\[
\theta = \tan^{-1}\left(\frac{126}{79}\right)
\]
Using a calculator to find this:
1. First, calculate the ratio:
\[
\frac{126}{79} \approx 1.5912
\]
2. Now, find the arctangent:
\[
\theta \approx \tan^{-1}(1.5912) \approx 57.7^\circ
\]
So, yes, you are correct that the angle of elevation is approximately \( 57.7^\circ \) when rounded to the nearest tenth of a degree.