math, trigonometry

a plane starts from a point P and flies 240km on a bearing of 120degrees to Q. At Q the plane makes a 90degree turn and flies back 100km on a bearing of 210degrees to R. At R the plane again changes direction and flies back to P.

The direct distance, in km, from R to P is?
the 3 figure bearing the pilot uses to fly from R to P is?

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  1. to find PR, use the Pythagorean Theorem, since angle Q is a right angle.
    Knowing PR, you can use the law of sines to find angle R.
    If you've drawn your diagram carefully, the bearing is 360-((angle R)-30)

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