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The angle of elevation of the top of a tower from two points at distances 9 m and 16 m from the base, in line with the foot, are complementary. The height of the tower is
A10 m
B15 m
C14 m
D12 m
Answer & Solution
Correct answer: D. 12 m
1. Let angles be theta and 90 minus theta; tan(theta) = h/9 and tan(90 - theta) = cot(theta) = h/16.
2. tan(theta) × cot(theta) = 1, so (h/9) × (h/16) = 1.
3. h squared = 144, hence h = 12 m.
_Source: NCERT Class 10 Mathematics, Ch 9 "Some Applications of Trigonometry", §9.2_
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