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).

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:

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