Question

A plane is heading due south with an airspeed of 211 mph. A wind from a direction of 53 degrees is blowing at 17 mph. Find the bearing of the plane. (Note that bearings are measured from north, clockwise.) Round results to appropriate number of significant digits.

Answer 1

Using cosine law we can find the velocity
v =sqrt(211² +17² -2•211•17•cos53º) = 201 mph.
Using sin law we can find the angle α
17/sinα =201/sin53º,
sin α = 17•sin53 º /201 = 0.0675.
α = 3.87 º.
Bearing
180 º – 3.87 º = 176.13º