PQRS are four locations on the same horizontal plane Q is an bearing of 041 degree from P and the distance is 40km,S is 28km from R on a bearing 074 degree, R is directly due north of P and the distant between Q and R is 38km. Find to the nearest whole number a. the bearing of R from P b. the distance between Q and S c. the distant between P and R
I need the diagram to explain better
As in all geometry problems, a detailed sketch will help you understand, and often solve, the problem.
Define P as the origin of the Cartesian plane.
Knowing that mPQ=40 km,
then coordinates of Q are given by
Q=P+40<cos(41),sin(41)>
=Q(30.188,26.242)
Similarly, R is directly north of P, and mQR=38, so there are two possible positions of R:
R1 is north of P, but below Q, and
R2 is north of P, but above Q.
So coordinates of R1:
R1=(0, Qy+sqrt(38²-Qx²))
=(0,26.242+23.079)
=(0,3.163)
and R2:
R2=(0, Qy+sqrt(38²+Qx²))
=(0,26.242+23.079
=(0,49.322)
Similarly, knowing mRS=28km, the coordinates of S1
S1=(R1+28<cos(74),sin(74)>
=(7.718,30.078)
and
S2=(R2+28<cos(74),sin(74)>
=(7.718,76.237)