Kyle stands 120 ft from the base of a tree. The angle of elevation from Kyle to the top of the tree is 48. What is the height of the tree to the nearest tenth of a foot?
Write the equation, and show all your work to solve for the indicated length.
We can use trigonometry to solve this problem. The tangent of an angle is equal to the opposite side over the adjacent side. In this case, the opposite side is the height of the tree and the adjacent side is the distance from Kyle to the base of the tree.
Let h be the height of the tree.
According to the information given, we have the following equation:
tan(48) = h / 120
To find h, we can rearrange the equation:
h = 120 * tan(48)
Using a calculator, we find:
h ≈ 120 * 1.1106
h ≈ 133.3
Therefore, the height of the tree is approximately 133.3 feet.