Geometry: triangles

Question

A hotel is 789 feet high. A 6ft tall man is standing on the roof and looking down at an island. If he is looking down at an angle of depression of 4 degrees, how far is the island from the hotel?

Answer 1

The heights of the hotel and man combined make up the vertical leg of the triangle.  The angle of depression is the angle between the distance the island is from the hotel and the mans vision.

 

tan(4) = (man's height + height of hotel) / (distance between island and hotel)

 

 

Solve for distance between island and hotel.

Answer 2

draw and label a diagram

d represents the distance of the island from the hotel

tan 4° = 795 / d

 

Can you solve for d?