Question

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?

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