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Answer:
The distance between X and Z is approximately 95.99 km
Step-by-step explanation:
- Given, X, Y and Z are three points on a map. Y is 85km and on a bearing of 190° from X. Z is on a bearing of 140°, from Y. Z is due south of X.
(For Diagram Please Find in Attachment)
- Thus, The parameters are
The distance of Y from X = 85 km
The bearing of Y from X = 190°
The bearing of Z from Y = 140°
The bearing of Z from X = 180°
Now,
- In triangle XYZ, we have
∠YZX = 180° - (130° + 10°) = 40°
- Therefore, Apply the sine rule here, we get
(85 km)/sin(40°) = XZ/(sin(130°))
XZ = sin(130°) × (85 km)/sin(30°) ≈ 95.99 km
The distance between X and Z ≈ 95.99 km
