SOLUTION: The pilot of a small plane finds that when the airspeed is 160 km/h and the heading is 295 degrees, the ground speed is 152 km/h and the course is 302 degrees. Find the speed and d

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Question 29268: The pilot of a small plane finds that when the airspeed is 160 km/h and the heading is 295 degrees, the ground speed is 152 km/h and the course is 302 degrees. Find the speed and direction of the wind.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Your directions of the original data are not given.

[v1] = 160cos(65)i + 160sin(65)j
[v2] = 152cos(58)i + 152sin(58)j
[vT] = [v1] + [v2]

[vT] = 149.17i +273.91j

||V|| = sqrt%28%28149.17%29%5E2%2B273.91%29%5E2%29
||V|| = sqrt%2897278.37%29
||V|| = 311.89

Use sine law to find the direction: (note: your units are not given, like north, west, east, south)

From sine law: sinT/160 = sin58/311.89
sinT=(160sin(58))/311.89
sinT = 0.435...
Take the inverse sin.
T=25.79

295-25.79=269.21

Hence, the speed of the plane is 311.89 making the direction of 269.21 or 90.79 degrees.
Paul.