Question

A pole being broken by the wind the top struck the ground at an angle of 30° and at a distance of 8m from the foot of the pole. Find the whole height of the pole.

Answer 1

Let ABC be the pole. When broken at B by the wind, let it's top A strike the ground such that
∠ CAB = 30°
AC = 8 m

In ΔACB,

tan 30° = `"BC"/"AC"`

`1/sqrt3 = "BC"/8`

`BC = 8/sqrt3`

Again In ΔACB,

cos 30° = `"AC"/"AB"`

`sqrt3/2 = 8/"AB"`

AB = `16/sqrt3`

Height of the pole = AC = AB + BC 

= `16/sqrt3 + 8/sqrt3`

= 8√3 m or 13.86 m.