Question

X, Y and Z are three points on a map. Y is 75km and on a bearing of 200° from X. Z is on a bearing of 150°, from Y. Z is due south of X. Calculate the distance between X and Z rounded to 1 DP.

Answer 1

Answer:

The distance between X and Z is approximately 114.9 km

Step-by-step explanation:

The given parameters are;

The distance of Y from X = 75 km

The bearing of Y from X = 200°

The bearing of Z from Y = 150°

The bearing of Z from X = 180°

In triangle XYZ, we have;

∠YZX = 180° - (130° + 20°) = 30°

By sine rule, we have;

(75 km)/sin(30°) = XZ/(sin(130°))

XZ = sin(130°) × (75 km)/sin(30°) ≈ 114.9 km

The distance between X and Z ≈ 114.9 km. to one decimal place.