A man whose eye is 180cm above the ground is standing 8m from a tree 7m tall. What is the angle of elevation of the tree from his eye?
We can use trigonometry to solve this problem.
Let the angle of elevation be θ.
Since the man's eye is 180cm above the ground, and he is 8m away from the tree, we can form a right triangle with the man's eye, the top of the tree, and the base of the tree.
The opposite side of the triangle is 7m (the height of the tree), and the adjacent side is 8m (the distance from the man to the tree). The hypotenuse is the distance from the man's eye to the top of the tree, which is 180cm + 7m.
Using the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = 7/8
So, θ = arctan(7/8)
θ ≈ 39.81 degrees
Therefore, the angle of elevation of the tree from the man's eye is approximately 39.81 degrees.