Question

AB is a straight road leading to a foot of tower at C. A being at the distance of 200m from C and B is 125m nearer. Angle of elevation of the top of tower at B is double than at A. So find the height of the tower.

Answer 1

Answer:

100 m

Step-by-step explanation:

Given AB is a straight road leading to a foot of tower at C. A being at the distance of 200m from C and B is 125m nearer. Angle of elevation of the top of tower at B is double than at A. So find the height of the tower.

Let the height of the tower be h, and it will be DC. Join AD and BD. Let angle A = x and angle B = 2x

tan x = h/200 or h = 200 tan x------------(1)

tan 2x = h/75 or h = 75 tan2 x

tan 2x = (2 tan x/1 - tan²x)

h = 75(2 tan x / 1 - tan²x)-----------------(2)

From (1) and (2) we get

200 tan x = 75(2 tan x /1 - tan²x)

1 - tan²x = 3/4

tan²x = 1/4

tan x = 1/2------------(3)

Substituting (3) in (1) we get

h = 200 x 1/2

h = 100 m

So the height of the tower is 100 m