Theory question 103
BearingsThe points X, Y and Z are located such that Y is 15 km south of X, Z is 20 km from X on a bearing of 270°. Calculate, correct to: (a) two significant figures, |YZ|; (b) the nearest degree, the bearing of Y from Z.
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Model answer
Sketch: Z is 20 km due west of X, Y is 15 km due south of X; ∠ZXY = 90°
(a) |YZ| = √(202 + 152) = √625 = 25 km
(b) At Z: tan θ = 15/20 → θ = 36.87° below east
Bearing of Y from Z = 90° + 36.87° ≈ 127°
Explanation
The right angle is at X, between the west and south directions.