Answer:
The two planes are 230 miles away after one hour.
Step-by-step 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
[tex]a = 200\ miles\\\\b = 300\ miles[/tex]
c = distance between both planes
Side c is opposite the angle of 50 °.
Then we use the law of cosine to find c.
[tex]c ^ 2 = a ^ 2 + b ^ 2 - 2abcos(50\°)[/tex]
[tex]c ^ 2 = 200 ^ 2 + 300 ^ 2 - 2*200*300cos(50\°)[/tex]
[tex]c = \sqrt{200 ^ 2 + 300 ^ 2 - 2*200*300cos(50\°)}[/tex]
[tex]c = \sqrt{52865.49}[/tex]
[tex]c = 230\ miles[/tex]
