Angle of depression from 50 m lighthouse — horizontal distance From the top of a lighthouse 50 m above sea level, the angle of depression of an approaching boat is 30°. How far is the boat from the lighthouse foot along the sea surface?

Introduction / Context:
Angle of depression equals the angle of elevation from the boat. With known vertical height, the horizontal distance follows from the tangent relation.

Given Data / Assumptions:

• Height h = 50 m.
• Angle of depression θ = 30° ⇒ tan θ = h/d.
• Calm sea assumed; straight line of sight.

Concept / Approach:
Let d be the horizontal distance. Then tan 30° = h/d ⇒ d = h / tan 30°.

Step-by-Step Solution:

Verification / Alternative check:
Numerically, √3 ≈ 1.732 ⇒ d ≈ 86.6 m, plausible for a 50 m elevation at 30°.

Why Other Options Are Wrong:
25√3 and 25/√3 correspond to halving the height; 50/√3 would be tan 60°, not tan 30°.

Common Pitfalls:
Inverting the tan ratio or confusing angle of depression with angle of elevation magnitude.

Final Answer:
50 √3 m