Question

The angle of elevation of the top of a tower from 2 points at a distance of 4m and 9m from base of the tower and in same straight line with it are complementary.prove that the height of the tower is 6m

Answer 1

for these quesion answer in the target

Answer 2

Que:- The angle of elevation of the top of a tower from 2 points at a distance of 4m and 9m from base of the tower and in same straight line with it are complementary.prove that the height of the tower is 6m

Solution:-

Since, Both are Complementary to each other.

=> If one is A, than other will be (90 - A).

In Triangle ABC,

Tan A = h/4 .........................(1)

In Triangle ABD,

Tan (90 - A) = h/9

Cot A = h/9 ...............(2)

Multiplying eq 1 and 2.

=> Tan A × Cot A = h/4 × h/9

=> Tan A × 1/Tan A = h^2/36

=> 1 = h^2/36

=> h^2 = 36

=> h = 6m.

Proved.