1. ## Trig problem solving

From the top of a cliff 185 m high, the angles of depression of two channel buoys in the same line of sight on the water are 13 degrees and 15 degrees. How far apart are the buoys?

I got approximately 6.86m but the answer says it 111m

2. Hello sinjid9
Originally Posted by sinjid9
From the top of a cliff 185 m high, the angles of depression of two channel buoys in the same line of sight on the water are 13 degrees and 15 degrees. How far apart are the buoys?

I got approximately 6.86m but the answer says it 111m
Study the attached diagram carefully, which shows the two angles of depression, and the equal (alternate) angles at water level.

Then, using the two right angled triangles:
$a = \frac{185}{\tan15^o}$

$b = \frac{185}{\tan13^o}$
and the distance apart is $b - a$.

Complete the calculation. You'll find the answer in the book is correct.