A pirate is on a hill looking at a building. The building is 400 feet tall. The angle of elevation from the pirate to the building is 4° and the angle of depression from the pirate to the bottom of the building is 2°. What is the shortest distance the pirate will need to travel to reach the building?

Question

A pirate is on a hill looking at a building.  The building is 400 feet tall.  The angle of elevation from the pirate to the building is 4° and the angle of depression from the pirate to the bottom of the building is 2°.  What is the shortest distance the pirate will need to travel to reach the building?

Steve · Answer

If the pirate is at horizontal distance x from the building, at the hill has height h, then

(400-h)/x = tan 4°
h/x = tan 2°
Eliminate h and you have

400 - x tan4° = x tan2°

Now you can find x. Assuming the pirate can fly horizontally, that is the shortest distance. Along the ground, no idea.