Question

The look-out point of a lighthouse is 50 feet above sea level. A woman observes a boat in the water from the look-out point. The angle of depression to the boat in the water is 20°.

What is the distance from the base of the light house to the boat in the water?

Round the answer to the nearest foot.

Answer 1

check the picture below.

make sure your calculator is in Degree mode.

Answer 2

Answer: The boat in the water is 137.37≈ 137 feet far away from the base of light house.

Explanation:

Since we have given that

Height of lighthouse above sea level = 50 feet

Angle of depression to the boat in the water = 20°

We need to find the distance from the base of the light house to the boat in the water.

So, it will form a right angled triangle:

Here, AB = 50 feet

∠ACB = 20°

So, we will use "Tangent of a triangle ":

`\tan 20^\circ=(AB)/(BC)\\\\\tan 20^\circ=(50)/(BC)\\\\BC=(50)/(\tan 20^\circ)\\\\BC=137.37\ feet`

Hence, the boat in the water is 137.37≈ 137 feet far away from the base of light house.