To find the angle of elevation of the top of the tree from the man's eye, we'll first identify the key information and use basic trigonometry (specifically, the tangent function) to solve the problem.
Here's a breakdown of the problem:
1. The height of the man's eye above the ground: 1.80 meters
2. The distance from the man to the tree: 8 meters
3. The height of the tree: 7 meters
The height difference between the top of the tree and the man's eye level is:
\[ \text{Height difference} = \text{Height of the tree} - \text{Height of the man's eye} \]
\[
\text{Height difference} = 7 \, \text{m} - 1.80 \, \text{m} = 5.20 \, \text{m}
\]
The angle of elevation \( \theta \) can be found using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where the "opposite" side is the height difference (5.20 meters) and the "adjacent" side is the distance from the man to the tree (8 meters).
So,
\[
\tan(\theta) = \frac{5.20}{8}
\]
To find \( \theta \), we take the arctangent (inverse tangent) of both sides:
\[
\theta = \tan^{-1}\left(\frac{5.20}{8}\right)
\]
Using a calculator to find the arctangent:
\[
\theta \approx \tan^{-1}(0.65) \approx 33.02^\circ
\]
Therefore, the angle of elevation of the top of the tree from the man's eye is approximately \( 33.02^\circ \).
A man whose eye is 180m above the ground is standing 8m from a tree 7m tall what is angle of elevation of the top of the tree from his eye
1 answer