Theory question 104
BearingsY 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.
Show the model answer
Model answer
(a) ∠YXZ = 225° − 135° = 90°, so |ZY| = √(602 + 802) = 100 km.
(b) tan ∠XYZ = 80/60, so ∠XYZ ≈ 53.1°. The bearing of X from Y is 315°.
Bearing of Z from Y = 315° − 53.1° ≈ 262°.
Explanation
Draw a sketch with north lines at X and Y; the angle at X is a right angle.