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The upper part of a tree is broken over by the wind and makes an angle of 42° with the ground. The horizontal distance from the root of the tree to the point where the top of tree meets the ground is 20 m. Find the height of the tree before it was broken.
Give your answer correct to the nearest whole number.

Heights & Distances

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Answer

Let AC be the broken part of tree.

The upper part of a tree is broken over by the wind and makes an angle of 42° with the ground. The horizontal distance from the root of the tree to the point where the top of tree meets the ground is 20 m. Model Question Paper - 2, Concise Mathematics Solutions ICSE Class 10.

In △ ABC,

⇒ tan 42° = ABBC\dfrac{AB}{BC}

⇒ 0.9004 = AB20\dfrac{AB}{20}

⇒ AB = 20 × 0.9004 = 18.008 m

⇒ cos 42° = BCAC\dfrac{BC}{AC}

⇒ AC = BCcos 42°\dfrac{BC}{\text{cos 42°}}

⇒ AC = 200.7431\dfrac{20}{0.7431} = 26.914 m

Height of tree = AB + AC = 18.008 + 26.914 = 44.9 ≈ 45 m.

Hence, height of tree = 45 m.

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