2023 · Q54
A person on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 minutes for the angle of depression to change from 30° to 45°, and further t minutes to reach the tower, which one of the following is correct?
Elementary MathematicsTrigonometry
- A7.7
- B8
- C8.3
- D8.6
Explanation
With tower height h, the car's distances from the base are h√3 at 30° and h at 45°. Covering h(√3 − 1) takes 6 minutes, so the remaining distance h takes 6/(√3 − 1) = 3(√3 + 1) ≈ 8.196 minutes. This lies in the interval 8 < t < 8.3 (B). (The transcribed options lost their range formatting; the original options were the intervals 7.7<t<8, 8<t<8.3, 8.3<t<8.6, 8.6<t<8.9.)