Hello, jasonk!

You can start by making a sketch . . .

3. The heading and air speed of an airplane are 60° and 250 mph, respectively.

The wind is 50 mph with a direction of 150°.

Find the ground speed and resulting course (direction) of the plane. Code:

P Q
: :
: : 150°
: B o
: * : * 50
: *60°:30°*
: 250 * : o C
: * : *
: * * :
: * * :
:60°* * R
: * *
A o

The plane's heading is:

The wind's heading is:

Note that

Then is the hypotenuse of right triangle

. .

In right triangle

. . then: .

Hence: .

Therefore, the plane's heading is 71.3° and its speed is 255 mph.