SOLUTION: The angle of elevation to the top of a tower from point A on the ground is 18.6 degrees . From a point​ B, 30.1 feet closer to the​ tower, the angle of elevation is 21.

Algebra ->  Trigonometry-basics -> SOLUTION: The angle of elevation to the top of a tower from point A on the ground is 18.6 degrees . From a point​ B, 30.1 feet closer to the​ tower, the angle of elevation is 21.      Log On


   

Question 1131838: The angle of elevation to the top of a tower from point A on the ground is 18.6 degrees . From a point​ B, 30.1 feet closer to the​ tower, the angle of elevation is 21.3 degrees . What is the height of the​ tower?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Two right triangles sharing a vertical side and the right angle.

x, the distance from bottom of tower to point B
y, distance to top of the tower from ground

system%28tan%2821.3%29=y%2Fx%2Ctan%2818.6%29=y%2F%28x%2B30%29%29

Solve the system to get y.

If you solve x in terms of y with one equation and substitute into the other equation, algebra steps should lead to:
highlight_green%28y=%2830%2Atan%2818.6%29%29%2F%281-tan%2818.6%29%2Ftan%2821.3%29%29%29.

You can compute that.