check out "kelvin" 's post at
https://www.jiskha.com/questions/1515062/P-Q-and-R-are-points-on-the-same-horizontal-plane-the-bearing-of-Q-from-P-is-150
P,Q and R are points on the same horizontal plane. The bearing of Q from P is 150 and the bearing of R from Q is 060. if PQ=5 and QR=3, find the bearing of R from P, correct to the nearest degree.
2 answers
All angles are measured CW from +y-axis,
PR = PQ + QR = 5[150o] + 3[60o],
X = 5*sin150 + 3*sin60 = 5.1,
Y = 5*Cos150 + 3*Cos60 = -2.83,
TanA = X/Y,
A = -61o = 61o E. of S. = 119o CW.
So the bearing of R from P = 119o.
PR = PQ + QR = 5[150o] + 3[60o],
X = 5*sin150 + 3*sin60 = 5.1,
Y = 5*Cos150 + 3*Cos60 = -2.83,
TanA = X/Y,
A = -61o = 61o E. of S. = 119o CW.
So the bearing of R from P = 119o.