Question

Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42°. How far is the boat from the base of the cliff

Answer 1

Answer: 338.73 feet.

Explanation:

1. You can draw a triangle as the right triangle you can see in the figure attached, where A is the point where Matt is and B is the point where the boat is.

2. Therefore, you can calculate the distance from the boat to the base of the cliff (This distance is identified as
`x` in the figure), as following:

`tan(42)=(opposite)/(adjacent)`

Where:

`opposite=305\\adjacent=x`

3. Substitute values and solve for
`x`:

`tan(42)=(305)/(x)\\x=(305)/(tan(42))\\x=338.73ft`