SOLUTION: From an observation tower that overlooks a runway, the angles of depression of Point A, on one side of the runway, and point B, on the opposite side of the runway are, 6 degrees an

Algebra ->  Trigonometry-basics -> SOLUTION: From an observation tower that overlooks a runway, the angles of depression of Point A, on one side of the runway, and point B, on the opposite side of the runway are, 6 degrees an      Log On


   

Question 1117519: From an observation tower that overlooks a runway, the angles of depression of Point A, on one side of the runway, and point B, on the opposite side of the runway are, 6 degrees and 13 degrees respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1.1 km. Determine the height of the tower
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x, from A to tower base
1.1-x, from B to tower base
y, tower height

Base, T, A, and B form two right triangles, sharing height y.

system%28y%2Fx=tan%286%29%2Cy%2F%281.1-x%29=tan%2813%29%29
Solve for y.

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a few algebra steps
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y=%281.1%2Atan%2813%29tan%286%29%29%2F%28tan%286%29%2Btan%2813%29%29