Changing depression from 30° to 45°: From the top of a vertical tower, a car approaches in a straight line on level ground. The angle of depression changes from 30° to 45° in 12 minutes. How much additional time is required (after it is 45°) for the car to reach the foot of the tower?

Introduction / Context:
With constant horizontal speed, times are proportional to horizontal distances. Angles of depression give those distances via tangent with the fixed tower height canceling out in ratios.

Given Data / Assumptions:

• Depression changes 30° → 45° in 12 min.
• Motion along the line toward the tower; level ground; constant speed.

Concept / Approach:
Let tower height be H (cancels). Horizontal distances: d30 = H / tan 30° = H√3; d45 = H / tan 45° = H. The 12 minutes correspond to d30 − d45. From 45° to the tower is d45. Time scales with distance at constant speed.

Step-by-Step Solution:

Verification / Alternative check:
Ratio method: T / 12 = d45 / (d30 − d45) = H / (H(√3 − 1)) → same value.

Why Other Options Are Wrong:
They correspond to rounding or formula mistakes; only ~16:23 matches exact evaluation of 6(√3 + 1) minutes.

Common Pitfalls:
Using depression distances incorrectly; forgetting to rationalize; rounding √3 too early leading to wrong seconds.

Final Answer:
16 min 23 sec.