Use the law of cosines

Question

Use the law of cosines

6. Two flying drones leave an airport at the same time. The heading of the
first is 120° and the heading of the second 320. If the drones are traveling
at 80 and 50 mph respectively, how far apart will they be after 1 hour?

Answer (Expert Verified)

The flying drones are illustrations of the laws of cosines

Both flying drones would be 128.13 meters apart after 1 hour

How to determine the distance between them

For drone A, we have:

  • Angle =120 degrees
  • Speed = 80 mph

So, the distance after one hour is:

Distance = 80 m

The distance is calculated using:

Distance = Speed * Time

For drone B, we have:

  • Angle = 320 degrees
  • Speed = 50 mph

So, the distance after one hour is:

Distance = 50 m

The angle between them is calculated as:

This gives

Using the laws of cosine, the distance (d) between them after 1 hour is:

So, we have:

Evaluate the expression

Hence, both drones would be 128.13 meters apart after 1 hour

Leave a Comment