Math

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?

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asked by Alexa
  1. 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.

    posted by Steve

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