To find the height of a tree, scientist Sally moves 160 feet away from the base of the tree and then, with a tool 6 feet tall, measures the angle of elevation to the top of the tree to be 62°. To the nearest foot, what is the height of the tree?
301 feet
301 feet
141 feet
141 feet
307 feet
307 feet
147 feet
To find the height of the tree, we can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle.
In this case, the opposite side is the height of the tree and the adjacent side is the distance from the base of the tree to Sally. The angle of elevation is the angle opposite the height of the tree.
Therefore, we can set up the following equation:
tan(62°) = height of the tree / distance from base of the tree to Sally
tan(62°) = height of the tree / 160 ft
Using a calculator, we can find that tan(62°) is approximately 1.8807268.
So, height of the tree = 1.8807268 * 160 ft
Height of the tree ≈ 300.92 ft
Rounding to the nearest foot, the height of the tree is approximately 301 feet.
Therefore, the nearest answer choice is 301 feet.