From point P on level ground, the angle of elevation of the top of a vertical tower is 30°. If the height of the tower is 100 m, find the horizontal distance of P from the foot of the tower (in metres).
Aptitude
Height and Distance
Difficulty: Easy
Choose an option
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A100 m
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B173 m
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C200 m
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D273 m
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E150 m
Answer
Correct Answer: 173 m
Explanation
Introduction / Context:This is a direct tangent application in a right triangle formed by the tower (vertical), the ground (horizontal), and the line of sight.
Given Data / Assumptions:
- Tower height h = 100 m.
- Angle of elevation θ = 30°.
Concept / Approach:tan θ = opposite / adjacent = h / x ⇒ x = h / tan θ.
Step-by-Step Solution:
tan 30° = 1/√3.x = 100 / (1/√3) = 100√3 ≈ 173 m.Verification / Alternative check:Back check: tan 30° = 100 / 173 ≈ 0.577? No—use exact √3: 100 / (100√3) = 1/√3 ✔ (≈ 0.577 inverse is 1.732 for √3).
Why Other Options Are Wrong:100 m assumes 45°; 200 or 273 m do not satisfy tan 30°; 150 m is an arbitrary round-off.
Common Pitfalls:Confusing sine and tangent; approximating √3 poorly; unit conversion is not needed here.
Final Answer:173 m