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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?

Sagot :

MrRoyal

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:

[tex]\theta = 360 -(320 - 120)[/tex]

This gives

[tex]\theta =160[/tex]

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

[tex]d = \sqrt{a^2 + b^2 -2ab\cos(\theta)}[/tex]

So, we have:

[tex]d = \sqrt{80^2 + 50^2 -2*80 *50\cos(160)}[/tex]

Evaluate the expression

[tex]d = 128.13[/tex]

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

Read more about laws of cosines at:

https://brainly.com/question/4372174

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