Question

Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is

200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
Reset
019 Edmentum A nohts reserved

Answer 1

The two planes are 230 miles away after one hour.

Explanation:

We know the speed of airplanes A and B and we know the angle between the speeds of both.

If the speed of plane A is 200 miles per hour, and the speed of plane B is 300 miles per hour, then after 1 hour the plane A will have traveled 200 miles and the plane B will have traveled 300 miles.

If we call c the distance between the two planes then we can use a triangle of sides, a, b and c

Where

`a = 200\ miles\\\\b = 300\ miles`

c = distance between both planes

Side c is opposite the angle of 50 °.

Then we use the law of cosine to find c.

`c ^ 2 = a ^ 2 + b ^ 2 - 2abcos(50\°)`

`c ^ 2 = 200 ^ 2 + 300 ^ 2 - 2*200*300cos(50\°)`

`c = √(200 ^ 2 + 300 ^ 2 - 2*200*300cos(50\°))`

`c = √(52865.49)`

`c = 230\ miles`