After 2 hours approximately distance between planes were 1217miles.
What is distance?
" Distance is defined as the length between two end points in one dimension."
Formula used
Cosine law
[tex]a^{2} =b^{2} + c^{2} -2bc cos A[/tex]
According to the question,
Plane 1 moves 20° east of north at 300 miles per hour
1 hour = 300 miles
2 hour = 600 miles
Plane 2 moves 40° east of south at 400 miles per hour
1 hour = 400 miles
2 hour = 800 miles
As shown in the diagram drawn we have,
Angle between two planes in 120°.
Substitute the value in cosine law to get the distance between planes,
[tex]a^{2} =(600)^{2} + (800)^{2} -2(600)(800) cos 120\°[/tex]
⇒[tex]a^{2} =360,000 +640,000 -(960,000)(\frac{-1}{2} )[/tex]
⇒[tex]a^{2} =1,480,000[/tex]
⇒[tex]a= 1216.55[/tex] miles
⇒ a ≈ 1217 miles (approximately)
Hence, after 2 hours approximately distance between planes were 1217miles.
Learn more about distance here
https://brainly.com/question/15172156
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