Question

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