An airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?

Question

Mathematics

Francis

22 February, 06:08

An airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?

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Barbara Patton · Answer 1

To find the new speed we will use the law of cousineTo find the direction law of sines will be usedx2=580^2+60^2-2 (580) (60) cos (75)

x = 567.44

sinθ60=sin75567.44

θ=5.86

N 54.14 degrees W is the true direction

true direction is N 54.14 degrees W