Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the :
(a) distance of Z from Y ;
(b) bearing of Z from Y.
Explanation
(a) < ZXY = 225° – 135°
= 90°.
(therefore /ZY/ = 80^{2} + 60^{2})
= (6400 + 3600 = 10000)
(/ZY/ = sqrt{10000})
= 100 km.
(b) From (Delta) XYZ,
(tan theta = frac{opp}{adj})
(tan theta = frac{80}{60} = 1.333)
(theta = tan^{-1} (1.333))
(theta = 53.13°)
Bearing of Z from Y = (360° – (45° + 53.13°))
= (360° – 98.13°)
= (261.87° approxeq 262°) (3 significant figures)