Depression changes from 30° to 60°: From the top of a 100 m tower, the angle of depression of a car is first 30° and later 60°. Assuming the car moves in a straight line toward the tower at constant level, find the distance the car travels between the two observations.

Introduction / Context:
Angles of depression equal angles of elevation from the same horizontal line. We compare two right triangles formed by the car’s positions and the tower height.

Given Data / Assumptions:

• Tower height H = 100 m.
• First depression = 30°; second depression = 60°.
• Car moves horizontally toward the tower on level ground.

Concept / Approach:
Horizontal distance d = H / tan(depression). The travel distance equals d1 - d2 between the two instants.

Step-by-Step Solution:

Verification / Alternative check:
Numeric: √3 ≈ 1.732 → 200/1.732 ≈ 115.47 m. This matches 200 √3 / 3 ≈ 115.47 m.

Why Other Options Are Wrong:
100 √3 and 200 √3 are too large; 100 √3 / 3 is half the correct value; only 200 √3 / 3 matches the geometry.

Common Pitfalls:
Using cot instead of tan (or forgetting that depression equals elevation), subtracting in wrong order, or mixing degrees and radians in calculators.

Final Answer:
200 √3 / 3