Trigonometric word problems

Question

The angle of elevation of the top of a fire tower from point A on the ground is 19.9 degrees. From point B, 50 feet closer to the tower, the angle of elevation is 21.8 degrees. What is the height of the tower?

Answer 1

Answer 2

Draw a figure.Let x be the height and y be the distance to the closer point.

Here is one way to do this problem, but I have a nagging suspicion there is an easier way.

tan 19.9 = x/(y+50) and tan 21.8 = x/y

which means (y+50)tan 19.9 = y tan 21.8.

Solve this for y and then use the value of y to get x.

If I think of the easier way later, I will get back to you.