Question

The angle of depression from the top of a 150 m high cliff to a boat at sea is 7 degrees. How much closer to the cliff must the boat move for the angle of depression to become 19 degrees

Answer 1

First: We can use tan to find x. If the original angle of depression is 7 degrees, then the angle from the cliff to the bow of the boat is 90-7=83 degrees. Thus,\[\tan83=\frac{d}{150}\]or\[d=150\tan83\approx855.2\]where d is the total distance from the boat to the cliff when the angle of depression is 7 degrees (see new drawing)