Question

From the top of the building, Ramesh is looking at a bicycle parked at some distance away from the building on the road.

If AB → Height of the building is 40 m, C → Position of bicycle,
A → Position of Ramesh on the top of the building.

∠MAC is the angle of depression and m∠MAC = 30°, then:

1. Draw a figure with the given information.
2. Find the distance between the building and the bicycle. (`sqrt3` = 1.73)

Answer 1

a.

b. m∠MAC = 30°      ...(Given)

∴ m∠ACB = 30°    ...(Alternate angles)

In ΔABC, m∠B = 90°

tan 30° = `"AB"/"BC"`

`therefore 1/sqrt3 = 40/"BC"`

∴ BC = 40`sqrt3`

∴ BC = 40 × 1.73

∴ BC = 69.20 m

The distance between the building and a bicycle is 69.20 m.