The surveyor in the forest tries to find the height of a tree using transit. He stands 120 ft away from the bottom of the tree and the angle of elevation to the top of the tree is 58 degrees. To the nearest foot, what is the height of the tree?
To find the height of the tree, we can use trigonometry.
Let h be the height of the tree. From the given information, we can form a right triangle with the height of the tree being the opposite side, the distance from the tree being the adjacent side, and the angle of elevation being 58 degrees.
Using the tangent function, we have:
tan(58 degrees) = h / 120 ft
h = 120 ft * tan(58 degrees)
h = 120 ft * 1.6643
h ≈ 199.72 ft
Therefore, to the nearest foot, the height of the tree is approximately 200 ft.