A cat is sitting on top of a tree, and spots a dog 10m south of the tree with an angle of depression of 65 degrees. Then it spots a firefighter a certain distance east of the tree with an angle of depression at 50 degrees. How far is the dog from the firefighter?

Question

i know the answer but have a hard time forming a mental image of what it looks like. drawing it does not help either.

Answer 1

we know the height h of the tree, since
tan65° = h/10

We know the distance d from the firefighter to the base of the tree, since
h/d = tan50°

Knowing d, the distance z from the dog to the firefighter can be found, since
z^2 = 10^2 + d^2
because the two lines of sight are perpendicular at the tree.