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
147 feet
147 feet
301 feet
301 feet
307 feet
307 feet
141 feet
To find the height of the tree, we can use trigonometry.
Let x be the height of the tree.
From the given information, we have the following right triangle:
/|
/ |
x / |
/ |
/ |
/ |
----- ------
160 6
tan(62°) = x/160
x = 160 * tan(62°)
x ≈ 306.6
To the nearest foot, the height of the tree is 307 feet. Therefore, the correct answer is 307 feet.