Question

From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.

Answer 1

Let CD is building A and B are two given points using horizontally on the same side of building.

In Δ DBC,

tan 60° = `"DC"/"CB"`

√3 = `10/y`                     .....(1)

In Δ DCA,

tan 30° = `"DC"/"CA"`

`1/(√3) = 10/(x + y)`            .....(2)

From (1), put y = `10/sqrt3` in (2), we get

`1/sqrt3 = 10/(x + 10/sqrt3)`

`1/sqrt3 = (10sqrt3)/(sqrt3x + 10)`

30 = √3x + 10

x = `20/sqrt3`

x = 11.55 m.

Hence, distance between two points A and B is 11.55 m.