Question

from the top of a tree the angle of depression of a rock on the ground is 49 degrees. If the tree is 18.5 m tall, how far is the rock from the base of the tree?

Answer 1

Answer:

Step-by-step explanation:

If you were to sit in the very top of said tree and look directly straight, your line of vision would be parallel to the ground. The angle of depression is in between your line of vision and the rock. When you look down at the rock, your line of vision to the rock is a transversal between the 2 parallel lines. With this being the case, the angle of depression is alternate interior with the angle made on the ground from the rock to the top of the tree. See the illustration I attached below.

We are looking for the distance on the ground between the tree and the rock, which we will call x. The side opposite the reference angle is the height of the tree and the side adjacent to the reference angle is x. Side opposite over side adjacent is the tangent ratio. Therefore,

$tan(49)=\frac{18.5}{x}$ and

$x=\frac{18.5}{tan(49)}$ and on your calculator in degree mode, you will find that

x = 16.08 m

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