Direct tan from distance and elevation — tower height A tower stands on level ground. From a point 100 m from its base, the angle of elevation of the top is 30°. What is the tower’s height?

Introduction / Context:This is a basic height–distance application of right-triangle trigonometry using the tangent function.

Given Data / Assumptions:

• Horizontal distance d = 100 m.
• Angle of elevation θ = 30°.
• Ground level and vertical tower.

Concept / Approach:In a right triangle, tan θ = opposite/adjacent = height/distance. Therefore, height h = d · tan θ.

Step-by-Step Solution:

Verification / Alternative check:As θ is small (30°), height should be less than distance, which it is (≈ 57.7 m).

Why Other Options Are Wrong:100√3 is too large; 100 m would imply tan 30° = 1; “None” is incorrect because 100/√3 is present.

Common Pitfalls:Using sin instead of tan; mixing up opposite and adjacent legs.

Final Answer:100/ √3