Question

A ship is sighted from the top of a lighthouse. The angle of depression from the lighthouse to the ship is 45degrees. The distance from the top of the lighthouse directly to the ship is 4miles.Calculate the horizontal distance of the ship from the bottom of the lighthouse

Answer 1

`2√(2) \text{ mi}`

Explanation:

See the attached image for a picture of the situation. The angle of depression lets you find the angle next to it but inside the triangle. It, too, must measure 45 degrees.

That means the triangle is an isosceles triangle (two legs of equal length).

Apply the Pythagorean Theorem.

`x^2+x^2=4^2\\2x^2=16\\x^2=18\\x=√(8)=2√(2)\approx 2.83\text{ mi}`