A man standing on the deck of a ship (25 m above water level) observes the angle of elevation of the top of a cliff as 60° and the angle of depression of the base as 30°. Find the height of the cliff.

Solution

Solution: Let the horizontal distance to the cliff be x. From the angle of depression, \(\tan30^\circ=\frac{25}{x}\), so \(x=25\sqrt{3}\) m. The height of the top above the observer is \(x\tan60^\circ=25\sqrt{3}\times\sqrt{3}=75\) m. Total cliff height \(=25+75=100\) m. Trick: Calculate the horizontal distance using the depression angle, then use the elevation angle to find the height above the observer.