An airplane is flying from montreal to vancouver. the wind is blowing from the west at 60km/h. the airplane flies at an airspeed of 750km/h and must stay on a heading of 65 degrees west of north. what heading should the pilot take to compensate for the wind? what is the speed of the airplane relative to the ground?

Refer to the diagram shown below.

In order for the airplane to maintain a heading of 65° west of north,  it actually heads at (65° +x) west of north at a speed of 750 km/h, to compensate for the wind blowing from west t east at 60 km/h.

The actual speed of the airplane relative to the ground is V km/h.

From geometry, obtain the triangle shown.
The speed of 750 km/h is opposite an angle of 155°, and the unknown angle x is opposite the wind speed of 60 km/h.

From the Law of Sines, obtain



The heading that the pilot should take is 65 + 1.937 = 66.94° west of north.

The third angle of the triangle is 180 - (155 + 1.937) = 23.063°.
Use the Law of Sines to calculate V.



The pilot heads approximately 67° (nearest integer) west of north.
The speed of the airplane relative to ground is 695.2 km/h (nearest tenth)