Question
If a tree has a height of 168 feet, what would be the angle of elevation from level ground measured from 58 feet away? Round your answer to the nearest tenth of a degree.
Answer
Attempt 1 out of 2
Answer
Attempt 1 out of 2
Answers
GPT-4o mini
To find the angle of elevation from a point on the ground to the top of the tree, we can use the tangent function in trigonometry. The angle of elevation is given by:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where:
- "opposite" is the height of the tree (168 feet),
- "adjacent" is the distance from the point where the angle is being measured to the base of the tree (58 feet).
Thus, we have:
\[
\tan(\theta) = \frac{168}{58}
\]
Now calculate \(\frac{168}{58}\):
\[
\frac{168}{58} \approx 2.89655
\]
Next, to find the angle \(\theta\), we take the arctangent (inverse tangent) of that value:
\[
\theta = \tan^{-1}(2.89655)
\]
Using a calculator to find the angle in degrees:
\[
\theta \approx 71.55 \text{ degrees}
\]
Now, rounding to the nearest tenth of a degree:
\[
\theta \approx 71.6 \text{ degrees}
\]
Therefore, the angle of elevation from level ground measured from 58 feet away is approximately **71.6 degrees**.
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where:
- "opposite" is the height of the tree (168 feet),
- "adjacent" is the distance from the point where the angle is being measured to the base of the tree (58 feet).
Thus, we have:
\[
\tan(\theta) = \frac{168}{58}
\]
Now calculate \(\frac{168}{58}\):
\[
\frac{168}{58} \approx 2.89655
\]
Next, to find the angle \(\theta\), we take the arctangent (inverse tangent) of that value:
\[
\theta = \tan^{-1}(2.89655)
\]
Using a calculator to find the angle in degrees:
\[
\theta \approx 71.55 \text{ degrees}
\]
Now, rounding to the nearest tenth of a degree:
\[
\theta \approx 71.6 \text{ degrees}
\]
Therefore, the angle of elevation from level ground measured from 58 feet away is approximately **71.6 degrees**.