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A tree breaks due to a storm and the broken part bends so that its top touches the ground 8 m from its foot. The angle the broken part makes with the ground is 30 degrees. The original height of the tree was
A8 ((square root of 3) + 1/(square root of 3)) m
B8 m
C24 m
D8 (square root of 3) m
Answer & Solution
Correct answer: A. 8 ((square root of 3) + 1/(square root of 3)) m
1. Standing piece has length p; broken piece has length q; p + q = original height.
2. tan(30) = p/8 gives p = 8/(square root of 3); cos(30) = 8/q gives q = 8/cos(30) = 16/(square root of 3).
3. Sum = 8/(square root of 3) + 16/(square root of 3) = 24/(square root of 3) = 8 (square root of 3); equivalent to 8 ((square root of 3) + 1/(square root of 3)) m.
_Source: NCERT Class 10 Mathematics, Ch 9 "Some Applications of Trigonometry", §9.2_
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