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.

Step-by-step 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:

$tan(42)=\frac{opposite}{adjacent}$

Where:

$opposite=305\\adjacent=x$

3. Substitute values and solve for $x$:

$tan(42)=\frac{305}{x}\\x=\frac{305}{tan(42)}\\x=338.73ft$