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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.
Solution
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.
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