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From the top of a tree, an observer sees a car approaching the base of the tree. The angle of depression of the car is initially 30°. Three minutes later, it increases to 60°. How much additional time will the car take to reach the tree?

1. 4 min.
2. 4.5 min.
3. 1.5 min
4. 2 min.

Correct answer: 1.5 min

Solution

The angle of depression indicates the observer's line of sight to the car, and as the angle increases from 30° to 60°, the car is getting closer to the tree. By using trigonometric relationships, we can determine the distances covered by the car during the initial time and the subsequent time, leading to the conclusion that it will take an additional 1.5 minutes to reach the base of the tree.

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