A cliff with a tower on its edge is observed from a boat at sea, the elevation of the top of the tower is 30 degrees. After rowing towards the shore a distance of 500 yards in the plane of the first observation, the elevations of the top and bottom of the tower are 60 degrees and 45 degrees respectively. Find the height of the cliff and the tower.

*A Treatise on Plane Trigonometry, *Ernest Hobson, 1891

Click here to reveal the answer

The answer is: the height of the tower is \(250(\sqrt{3}-1) \approx \) 183 yards, and the height of the cliff is 250 yards.