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Question
A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance 30 m from the root. Find the whole height of the tree. (`sqrt(3)`=1.73)
Solution
Let AB represent the height of the tree.
Let the tree break at point C.
AC is the broken part of the which takes position CD such that ∠CDB = 30°
∴ Ac = CD ....(1)
In right-angled ΔCBD,
tan 30° = `(BC)/(BD)`
∴`1/sqrt(3) = (BC)/30`
∴ BC = `30/sqrt(3)`
cos 30° = `(BD)/(CD)`
∴ `sqrt(3)/2 = 30/(CD)`
∴ `sqrt(3) xx CD = 30 xx2 `
∴CD `60/sqrt3`
Ab = AC + BC .....[A-C-B]
∴ AB = CD + BC ... [From (i)]
∴ AB =`60/sqrt3 + 30/ sqrt 3`
∴ AB = `90/sqrt3 = 90/ sqrt3 xx sqrt3/ sqrt3` ....[Rationalizing the denominator]
∴ AB `(90sqrt3)/3 = 30sqrt3 = 30 xx 1.73 = 51.9` m
∴ Height of the tree is 51.9 m.
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