Question

In five minutes, you observe that the angle of elevation of a hot air balloon, climbing vertically, changes from 25° to 60°. If you were standing 300 meters away from the take off point, how many meters did the balloon travel in that time?

Answer 1

379.72 meters

Explanation:

At first, the balloon was 300 m away at 25°, so its height can be determined as:

`H_(1) = 300*tg(25)\\H_(1) = 139.89 m`

After 5 minutes, the balloon was at 60°, so its height can be determined as:

`H_(2) = 300*tg(60)\\H_(1) = 519.61 m`

To find the distance traveled by the balloon during that period, simply subtract the second height by the first one:

`d= H_(2) -H_(1) \\D= 519.61 - 139.89 \\D=379.72`

The balloon traveled 379.72 meters in that time.