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A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60º with the horizontal. Find the height of the tree.[Figure: vertical broken tree AB with base A; the broken top rests on the ground at C, 20 m from A, wi…

Q.3 (B)(3) A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60º with the horizontal. Find the height of the tree.

[Figure: vertical broken tree AB with base A; the broken top rests on the ground at C, 20 m from A, with ∠BCA = 60º, where B is the point where the tree broke.]

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Answer: height of the tree ≈ 74.64 m

Let AB be the standing part and BC the broken part lying on the ground, AC = 20 m, ∠BCA = 60º, ∠BAC = 90º.

In right Δ BAC, \(\tan 60^\circ = \dfrac{AB}{AC}\), so AB = \(20\sqrt3\) = 34.64 m.

\(\cos 60^\circ = \dfrac{AC}{BC}\), so BC = \(\dfrac{20}{\cos 60^\circ} = \dfrac{20}{1/2}\) = 40 m.

Height of the tree = AB + BC = 34.64 + 40 = 74.64 m.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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