how to find the bearing of the wind in question

Question

An airplane heads N60E at a speed of 600 mi/h relative to the air. A wind begins to blow in the direction N 30 W at 50 mi/h. Find the true speed and direction of the airplane. 

Answer 1

It helps if you draw the two vectors; in standard trigonometry, they are:

 

Wind:     50 cis 120^o = <-25, 25√3>

Aircraft: 600 cis 30^o = <300√3, 300>

 

Adding these two vectors gives <494.615, 343.301>

 

Since the angle between these two vectors equals 90 degrees, the Pythagorean Theorem is used to find the resultant magnitude: 602.08

 

the angle relative to the standard initial side (on the x-axis for 0 degrees due E) in trigonometry is θ = arctan (343.301/494.615) = 34.76⁰ OR n 55.24^O E.