Question

Can you help me with this question?

Answer 1

Answer: 359 ft

Step-by-step explanation:

Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea).  This allows you to create a right triangle (see attached image).

The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building.  Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.

NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!

Now you can use trigonometry to solve ....

In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.

$tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 24^o=\dfrac{160}{x}\\\\\\\rightarrow x=\dfrac{160}{tan\ 24^o}\\\\\\\rightarrow x=359.4\\\\\\\rightarrow x\approx 359$