Question

A man standing on a lighthouse at a height of 124 feet sights two boats directly in front of him. One is at an angle of depression of 62°, and the other is at an angle of depression of 33°. Identify the distance between the two boats. Round your answer to the nearest foot.

Answer 1

Answer:

$125\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ABC find the length side BC

we know that

$tan(62\°)=\frac{124}{BC}$

$BC=\frac{124}{tan(62\°)}$

step 2

In the right triangle ABD find the length side BD

we know that

$tan(33\°)=\frac{124}{BD}$

$BD=\frac{124}{tan(33\°)}$

step 3

we know that

The distance between the two boats is the length side CD

$CD=BD-BC$

substitute the values  

$CD=\frac{124}{tan(33\°)}-\frac{124}{tan(62\°)}=125\ ft$