The bearing of Y from X is 060º and the bearing of Z from Y = 060º. Find the bearing of X from Z

Analyze the question: We are given the bearing of Y from X (060°) and the bearing of Z from Y (060°). We want the bearing of X from Z.

Concept: A back bearing differs from the forward bearing by 180°.

• If the forward bearing is less than 180°, add 180°.
• If it is more than 180°, subtract 180°.

Solution:

1. Place X at the origin. Y is on a bearing of 060° from X.
2. From Y, Z is on a bearing of 060° again. So X, Y and Z are on the same straight line, because both legs go in the same direction (060°).
3. The bearing of Z from X is therefore also 060°.
4. The bearing of X from Z is the back bearing of this line:

060° + 180° = 240°

Check: Since the path X → Y → Z is a straight line in direction 060°, coming back from Z to X means travelling in the opposite direction, which is 240°.

Answer: The bearing of X from Z is 240°, which is option B.

Tip: When two consecutive bearings are equal, the three points lie on one straight line. Just find the back bearing by adding 180° (if the angle is below 180°) or subtracting 180° (if it is above 180°).