What is the true course of the plane in degrees?

Question

A plane headed due east is traveling with an airspeed of 210 miles per hour. The wind currents are moving with constant speed in the direction 240°. If the ground speed of the plane is 105 miles per hour, what is its true course?

 __°

Answer 1

If you draw this, note that 105 is half of 210. Also, note that the 240° angle is from due N. Then, using this system, due E is a 90° angle, so the 240° angle is 150° clockwise from the 90° angle. This means the internal angle is 30°.

Thus, we can note that, with one length 210 and another length opposite the 30° angle of 105 a 30-6, we have a 30-60-90 triangle - 105/210 = sin 30°/sin x, so 105 sin x = 105, so x = 90°. Then, the third angle made up of the air direction and the ground direction, will be 60°. As this will be clockwise from due East, the true course will be 90° + 60° = 150°.