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प्रश्न
The top of a palm tree having been broken by the wind struck the ground at an angle of 60° at a distance of 9m from the foot of the tree. Find the original height of the palm tree.
बेरीज
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उत्तर
Let AC was original tree. It was broken into two parts. The broken part A' B is making 60° with ground.
In ΔA'BC
`"BC"/"A'C" = tan 60^circ`
`"BC"/9 = sqrt(3)`
`BC = 9sqrt(3)`
`"A'C"/"A'B" = cos 60^circ`
`9/"A'B" = 1/2`
`A'B = 18`
Height of tree = A'B + BC
= `9sqrt(3) + 18 = 9 × 1.732 + 18 = 15.588 + 18 = 33.588`
Hence , the height of tree was 33.588 m = 33.6 m (approximately).
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