Question

A cat, sitting on top of a tree, spots a dog and a firefighter, both on flat ground below. From the cat's point of view, the dog is 10m south, at an angle of depression of 65 degrees, and the firefighter is some distance east of the tree, at an angle of depression of 50 degrees. How far is the firefighter from the dog?

Answer 1

The height h of the tree is given by

h/10 = tan 65°

Now, having h, you can get the distance f of the firefighter:

f/h = cot 50°

Now, the distance d between the dog and the firefighter is

d^2 = 10^2+f^2