Asked by Pamela
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
angle PQR = 180 degrees - 160 degrees = 20 degrees
Answers
Answered by
Steve
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°
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°
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