Three police posts X, Y and Z are such that Y is 50km on a bearing 060 degrees from X while Z is 70km from Y and on a bearing of 300 degrees from X.

Question

Three police posts X, Y and Z are such that Y is 50km on a bearing 060 degrees  from X while Z is 70km from Y and on a bearing of 300 degrees from X.
 
Determine the distance, in km, of Z and X.

oobleck · Accepted Answer

Draw triangle XYZ, with sides x,y,z in the usual places, ooposite the angles.
That is, XZ = y
Using the law of sines,
z/sinZ = x/sinX
50/sinZ = 70/sin120°
Now, knowing X and Z, it's easy to find Y, and you can use either law of sines or law of cosines to find XZ = y

henry2, · Answer

All angles are measured CW from +y-axis XZ = XY + YZ = 50[60o] + 70[300o]. XZ = (50*sin60+70*sin300) + (50*cos60+70*cos300)I, XZ = -17.3 + 60i = 62.4km[-16o] = 62.4km[344o] CW.