Question

Find the height of a building, when it is found that on walking towards it 40 m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°.

Answer 1

Let AB be the building of height h m. 

Let the two points be C and D such that CD = 40 m, ∠ADB = 30° and ∠ACB = 45°

In ΔABC,

`(AB)/(BC) = tan 45^circ = 1`

`=>` BC = h

In ΔABD,

`(AB)/(BD) = tan 30^circ`

`=> h/(40 + h) = 1/sqrt(3)`

`=> sqrt(3)h = 40 + h`

∴ `h = 40/(sqrt(3) - 1)`

= `40/(0.732)`

= 54.64 m

Hence, height of the building is 54.64 m.