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).

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:

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