Acat, sitting in the top of a tree, spots a dog and a firefighter both on the flat ground below. from the cats point of view , the dog is 10 meters south from the base of the tree, 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?

15 meters

Step-by-step explanation:

Denote points: C - cat, B - base of the tree, D - dog, F - Firefighter.

Consider triangle CBD. This triangle is right triangle with right angle CBD and m∠BCD=65°, DB=10 m. Then

Consider right triangle CBF. In this triangle angle CBF is right angle and m∠CFB=50°, then

Consider right triangle BDF. In this triangle angle FBD is right and by the Pythagorean theorem,

the answer is 1030 it's very simple math.