Question

If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is
A. ab
B. √ab
C. a/b
D.√a/b

Answer 1

The height of the tower is :

• Given : The angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary.

• Angle of elevation from distance a = Θ

• Angle of elevation from distance b = 90 - Θ

• In ∆PQR,

tan (90 - Θ) = h/b

cot Θ = h/b .... (1)

• In ∆SQR,

tan Θ = h/a ....(2)

• Multiply (1) and (2)

cot Θ×tan Θ = h^2 / ab

1/tanΘ×tanΘ = h^2 / ab

1 = h^2 / ab

h^2 = ab

=> h = √ab m

Answer 2

Answer:

Check your answer please