A pilot wishes to fly from his home field to a destination 625km S20E. The cruising speed of the aircraft is 535 km/h. If there is a wind of 72km/h blowing from N80W, what heading should the pilot take in order to reach his destination and how long will the flight take (to the nearest minute)?
If you make a sketch, you see that the heading should be more towards the south and the angle between the straight line to the destination and the line showing the wind is 90-(10+20) = 60 degrees.
Now, use the sine rule...
You should get A = 6.69 degrees.
Therefore, the heading is 20 - 6.69 = 13.3 degrees, and in your notation, S13.3E.
Then, find the resultant speed. To do this, find the last angle of the triangle.
Angle = 180 - (60+6.69) = 113.7 degrees.
Then either by sine rule or cosine rule, find the last side of the triangle.
I'll use the cosine rule.
Speed = 567 km/hr.
Hence, time of travel = 625/567 = 1.10 hour or 1 hour 6 minutes