A 15-meter tower's top makes a 60° elevation angle with an electric pole's base and a 30° angle with its top. Find the pole's height.
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Answer: C. 10 metres
Explanation
Using trigonometric tangent ratios with the sixty degree angle establishes the horizontal distance to the pole. Applying the thirty degree angle of elevation from the tower top determines the height difference. Combining the geometric height segments yields the exact electric pole height of ten meters. Trigonometry uses angle of elevation measurements to calculate unknown heights and distances indirectly. The tangent of an angle in a right triangle equals the opposite side divided by the adjacent side. Vertical height problems involving towers and poles require establishing a shared horizontal baseline.
Civil engineers calculate heights of tall structures and terrain features using theodolite sighting angles. Surveyors determine building clearances and utility pole dimensions without direct physical measurement. Navigation systems use triangulation principles to establish relative positions of distant landmarks. Option a underestimates the pole height by misapplying the thirty degree tangent ratio. Option b results from an arithmetic error in the horizontal distance calculation steps. Option d overestimates the height by treating the angle relationships incorrectly.
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- Mathematics
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- Mathematics
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- Difficulty
- medium
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