The angles of elevation of the top of a tower from two points

• Quant Trigo

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

1. 48 m
2. 30 m
3. 25 m
4. 24 m

Answer

If one angle is A, then other will be (90 - A)

Tan A = h/36

Tan (90 - A) = h/64

Cot A = h/64

Tan A = 64/h = h/36

h² = 64*36

h = 8*6 = 48

The correct option is A.