Question

A person is watching a boat from the top of a lighthouse. The boat is approaching
the lighthouse directly. When first noticed, the angle of depression to the boat is
17°31. When the boat stops, the angle of depression is 46°41: The lighthouse is 200
feet tall. How far did the boat travel from when it was first noticed until it stopped?
Round your answer to the hundredths place. (3 points)

Answer 1

9514 1404 393

Answer:

  445.10 feet

Step-by-step explanation:

The relation between angle of depression and distance to the boat is ...

  Tan = Opposite/Adjacent

  tan(angle of depression) = (200 ft)/(distance to boat)

Then the distance to the boat is ...

  distance to boat = (200 ft)/tan(angle of depression)

__

We want the change in distance between the two angles, so ...

  change in distance = (200 ft)/tan(17°31') -(200 ft)/tan(46°41')

  = (200 ft)(cot(17°31') -cot(46°41'))

  change in distance ≈ 445.10 ft