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| =5m and |QR|=3m find the bearing of R from P correct your answer to the nearest degree

Answer 1

In geometry, drawing a sketch from given information is half-way to the solution.

Note bearing is measured clockwise from North.

If you draw the sketch in Cartesian coordinates, using P at the origin, you will have
P(0,0)
Bearing 150°≡ θ=90-150=-60° in Cartesian coordinates.
So
Q(5cos(-60), 5 sin(-60))
=Q(2.5, -2.5&radic/3)

Similarly, the bearing of R from Q is 60°≡ θ=90-60=30°.
So
Δx=3cos(30)=1.5√3
Δy=3sin(30)=1.5

Therefore the coordinates of R relative to P
R(2.5+Δx, -2.5&radic/3+Δy)
=R(2.5+1.5√3, -2.5√3+1.5)

Bearing of R from P
=90-atan(y/x)
=90-atan((-2.5√3+1.5)/(2.5+1.5√3))
=90-(-29)
=119°