Single observation with known height: 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.

Introduction / Context:Relating a known vertical height and an observed angle of elevation to a horizontal distance uses the tangent definition in right-triangle trigonometry.

Given Data / Assumptions:

• Height H = 100 m.
• Angle of elevation θ = 30°.
• Horizontal distance from point to foot = d (unknown).

Concept / Approach:tan θ = opposite / adjacent = H / d → solve for d.

Step-by-Step Solution:

Verification / Alternative check:Compute tan using result: 100 / (100√3) = 1/√3 → 30°, correct.

Why Other Options Are Wrong:100/√3 would imply tan 30° = √3, which is inverted; 50√3 or 50/√3 do not match the given 100 m height.

Common Pitfalls:Confusing tan with cot; swapping opposite and adjacent; rounding √3 too early; answer needs exact form unless asked otherwise.

Final Answer:100 √3 m