Question

Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be 30° and 38° respectively. Find the distance between them, if the height of the tower is 50 m.

Answer 1

Two persons A and B are standing on the opposite side of the tower TR and height of tower TR = 50 m and angles of elevation with A and B are 30° and 38° respectively.

Let AR = x and RB = y

Now in right ΔTAR, we have

`tan theta = (TR)/(AR)`

`=> tan 30^circ = 50/x`

`=> 1/sqrt(3) = 50/x `

∴ `x = 50sqrt(3) = 86.60  m`

Again in right ΔTRB, we have

`tan 38^circ = 50/y`

`=>` y tan 38° = 50

`y = 50/tan 38^circ`

= `50/0.7813`

= 63.99

or 64.00 m   ...(i)

∴ Distance between A and B

= x + y

= 86.60 + 64.00

= 150.6 m