Trigonometry
posted by Marika on .
From an observation tower that overlooks a small lake, the angles of depression of point A, on one side of the lake, and point B, on the opposite side of the lake are, 7degrees and 13degrees, respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1km. Determine the height of the tower.

I made a side view diagram, with A and B the points on the lake, obviously A farther away from the tower. I labeled my tower DC , C as the base of the tower.
In Triangle ABD, angle A = 7°, angle ABD = 167° , angle ADB = 6° , and AB = 1 km
by the sine law:
BD/sin7 = 1/sin6
BD = sin7/sin6 = 1.16589... (keep number in calculator's memory)
Now in the rightangled triangle, BCD
DC/BD = sin13
DC = 1.16589..(sin13) = .26226 km
or appr 226 m 
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