Question

Two forest rangers each spot smoke from their observation towers. The first ranger determines ZCAB-82°. The second ranger determines that ZCBA-67. Which ranger is closest to the smoke area? How do you know?​

Answer 1

The second ranger is closest to the smoke area.

We can determine this by using the following information:

The first ranger determines ZCAB-82°.

The second ranger determines that ZCBA-67.

This means that the first ranger is looking at the smoke from an angle of 82 degrees, while the second ranger is looking at the smoke from an angle of 67 degrees. Since a smaller angle indicates that the object is closer, the second ranger must be closer to the smoke area.

Another way to think about this is to imagine that you are standing in the middle of a field and two friends are standing on opposite sides of the field. If one friend is looking at you from an angle of 82 degrees and the other friend is looking at you from an angle of 67 degrees, it is clear that the second friend is closer to you.

Therefore, the second ranger is closest to the smoke area.

Answer 2

In this case, ZCBA (67°) is the smaller angle compared to ZCAB (82°). So, the second ranger (ZCBA) is indeed closer to the smoke area

Explanation:

To determine which ranger is closer to the smoke area, you should look at the smaller angle between the lines of sight to the smoke. The ranger with the smaller angle has a narrower field of view and is closer to the source of the smoke.

In this case, ZCBA (67°) is the smaller angle compared to ZCAB (82°). So, the second ranger (ZCBA) is indeed closer to the smoke area. Smaller angles between the lines of sight indicate closer proximity to the source of the smoke.