Some Applications of Trigonometry

Some Applications of Trigonometry

Question

The angle of elevation of the top of a hill at the foot of a tower is 600 and the angle of depression from the top of the tower of the foot of the hill is 300. If the tower is 50 m high, find the height of the hill.

Answer

                           

Let the height of hill is  h.

In right triangle ABC,

50AB = tan300 50AB = 13 AB = 503In right triangle ABD,hAB = tan600  hAB = 3 h = 3 AB h = 3 503 = 150 m.

Hence the height of hill is 150 m.

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