Question

town Q is on a bearing 210°from town P. R is on a bearing 150° from town P and R is east of Q. The distance between R and P is 10km. Find the distance between R and Q.

Answer 1

<b>sketch it</b>. you know in the triangle angle P, and angle Q just from the bearings. I get
P=210-150
Q=60 (QR is due East)

so you have two (three if you consider the entire triangle), one opposite side. Law of sines is useful at this point

Answer 2

Vector Q makes an angle of 60o with the -X-axis.
Vector R makes an angle of 60o with the +X-axis.
Each vector forms a 60-30 right triangle.

Using vector R, Cos60 = X/r = X/10, X = 10*Cos60 = 5 km.
sin60 = Y/r = Y/10, Y = 8.66 km. = Ver. component of R and Q.

Using Vector Q, Tan60 = Y/X = 8.66/X, X = 5 km.
QR = 5 + 5 = 10 km = Distance between R and Q.