Question
A tree breaks due to storm and the broken part bends, so
that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree (in metres)Solution
BC = 12 m Height of the tree = AB + AC Tan 30° = AB/12 ⇒ (1/√3) = AB/12 ⇒ AB = (12/√3) Cos 30° = BC/AC = 12/AC ⇒ √3/2 = 12/AC ⇒ AC = 24/√3 Hence, AB + AC = 12/√3 + 24/√3 = 36/√3 ⇒ 36/√3 × √3/√3 (rationalizing to remove root from denominator) ⇒ 36√3/3 = 12√3 ∴ Height of the tree = 12√3 m
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