John wishes to determine the height of a flagpole. He takes a sighting of the top of the flagpole from point P. He then moves further away from the flagpole by 20 metres to point Q and takes a second sighting. Given the angle Q is 28 degrees and angle P is 53 degrees.

Question

Find how high is the flagpole?

Answer 1

If P is x meters from the base of the pole of height h, then

h/x = tan 53°
h/(x+20) = tan 28°

eliminate x and you have

h cot 53° = h cot 28° - 20
h = 20/(cot28°-cot53°)