Question

A pole of height 30 m is observed from a point. The angle of depression of the point is 30°. Find the distance of the point from the base of the pole.

Answer 1

Let XY be the pole and Z be the position from which the pole is observed.

MXZ and ∠XZY are alternate angles.

Now, in ΔXYZ,

tan 30° = `(XY)/(YZ)`

⇒ `1/sqrt(3) = 30/(YZ)`

⇒ YZ = `30sqrt(3)`

As a result, the distance between point Z and the pole's base is  `30sqrt(3)` m.