Question

height of the tower is 6 m.
Q. 3. The angles of elevation of the
top of a tower from two points at a
distance of 4 m and 9 m from the base of
the tower and in the same straight line
with it are complementary. Prove that the
1200 Serie​

Answer 1

Correct Question:

The angles of elevation of the

top of a tower from two points at a

distance of 4 m and 9 m from the base of

the tower and in the same straight line

with it are complementary. Prove that the

height of the tower is 6 m.

Step-by-step explanation:

( Refer attachment )

In ∆ABC

tan (alpha) = AB/BC ..............(1)

In ∆ABD

tan (beta) = AB/BD

tan (beta) = AB/(BC + CD)

As alpha and beta are supplementary. So,

alpha + beta = 90°

beta = (90° - alpha)

Therefore,

tan (90° - alpha) = AB/(BC + CD)

cot (alpha) = AB/(BC + CD)

1/tan(alpha) = AB/(BC + CD)

tan (alpha) = (BC + CD)/AB

tan (alpha) = BD/AB .............(2)

On comparing (1) & (2) we get,

→ AB/BC = BD/AB

→ AB(AB) = BD(BC)

→ (AB)² = BD(BC)

Substitute the values,

→ (AB)² = 9(4)

→ (AB)² = 36

→ AB = 6

Hence, the height of the tower is 6 m.