# math

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A ship leaves POrt P and sails 28km away on bearing of 70 degrees to POrt Q. The ship then turns on a bearing of 160 degrees and sails 21km to POrt R. Find angle PQR, calculate the distance PR, Determine the bearing of R from P.

angle PQR = 180 degrees - 160 degrees = 20 degrees

• math -

ships sail on headings, not bearings.

Angle PQR is not the angle between the NS line and R. It is the angle between PQ and QR. That is, 70 + 20 = 90 degrees.

So, now we can figure the x-y displacements:

PQ = <28sin70°,28cos70°> = <26.31,9.58>
QR = <21sin20°,-21cos20°> = <7.18,-19.73>

Add them up and you get PR = <33.49,-10.15> = 35.00 at 106.88°

• math -

Dp yygg

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