Problema Solution
A man is standing in a lighthouse watching for ships. He sees a ship coming in and measures its distance from the cliff he is on. He knows that he is standing 340 feet above the waves and he measures the angle of depression from him to the ship at 40 degrees.
How far is the ship from the base of the cliff? (The lighthouse is on top of the cliff.)
The man in the lighthouse knows there are dangerous rocks only 82 feet from the shore. How far is the ship from hitting the rocks?
Answer provided by our tutors
let d = the distance of the ship from the base of the cliff
make a good drawing and notice the right triangle with the right angle at the base of the cliff
tan 40 = d/340
d = 340*(tan 40)
d = 285.29 ft
the ship is 285.29 ft away from the base of the cliff
d - 82 = 285.29 - 82 = 203.39 ft
the ship is 203.39 ft far from hitting the rocks.