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Expert: - 5/31/2010


Question
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To fly due north at 580km/h when there is a 45km/h wind blowing from 130degrees, with what heading and speed should a plane travel?


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A plane's air speed is 270 km/h, and its heading is 70degrees. Find its ground speed and true-course bearing if a wind of 50 km/h is blowing from due north.

These are the only two I'm stuck on.
Thanks so much for taking the time to help me.
Thank You!

Answer
Both of these follow the rule a² + b² = c² - 2abcos(C),
where C is the angle between sides a and b.

For this kind of problem, it is good to makes sure the problem is using degrees.
To check, sin(90°) = 1.  In radians, it will say sin(90) = 0.893996664.

A is the angle opposite side a and B is the angle opposite side C.
Side a is the one going due north.

On the first one, a is 580 and the b is 45.
The angle between a and b is C, and that is 130°-90°=40°.

Side c can be found by a² + b² + 2abcos(C) = c².
Once this has been done, angle A can be found with the law of sines, that is, a/sinA = c/sinC.
Angle A would be how far off north the angle is.

For the second problem, let a=270 and b=50.
Thane angle on b is true north, which is 90°,
so side a is 20° from this, so that is angle C.

Using a² + b² + 2abcos(C) = c², c can be found.
Using sinA/a = sinC/c, angle A can be found.

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