On level ground, the angle of elevation of the top of a tower is 30°. After moving 20 m nearer the tower, the angle increases to 60°. Find the height of the tower (in metres).

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Two elevation angles from positions 20 m apart allow solving the system for both distance and height via tangent relations. Given Data / Assumptions: Initial angle = 30° at distance x. Second angle = 60° at distance x − 20. Height h unknown. Concept / Approach:Write h = x * tan 30° and h = (x − 20) * tan 60°. Equate to eliminate h and solve for x, then back-substitute to get h. Step-by-Step Solution: x * (1/√3) = (x − 20) * √3.x = 3(x − 20) ⇒ x = 3x − 60 ⇒ 2x = 60 ⇒ x = 30 m.h = x / √3 = 30/√3 = 10√3 m. Verification / Alternative check:At x − 20 = 10 m, tan 60° = h/10 ⇒ h = 10√3 ✔; all consistent. Why Other Options Are Wrong:10, 15, 20, 30 m ignore √3 relationships intrinsic to 30°/60° pairs. Common Pitfalls:Using x + 20 instead of x − 20 for “moved nearer”; mixing degrees and radians in calculators. Final Answer:10√3 m

On level ground, the angle of elevation of the top of a tower is 30°. After moving 20 m nearer the tower, the angle increases to 60°. Find the height of the tower (in metres).

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