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?(1 point) Responses 307 feet 307 feet 147 feet 147 feet 301 feet 301 feet 141 feet
To find the height of the tree, we can use the tangent function.
Let h be the height of the tree.
According to the problem, Sally is 160 feet away from the base of the tree, and the tool she is using is 6 feet tall. This creates a right triangle with the tree's height as the opposite side, the distance from Sally to the base of the tree as the adjacent side, and the tool's height as the opposite side.
Using the tangent function, we have:
tan(62°) = h/160
To find h, we can rearrange the equation:
h = tan(62°) * 160
Using a calculator, we find:
h ≈ 307 feet
Therefore, the height of the tree is approximately 307 feet.