WAEC Mathematics 2021 Theory — Question 4
Question 4 of 22 from the West African Examinations Council (WAEC) Mathematics 2021 Theory paper, with the correct answer and a full explanation.
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3. The points X, Y and Z are located such that Y is 15 km south of X, and 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.
Model answer
Since XY (south) and XZ (due west, bearing 270°) are perpendicular, by Pythagoras: |YZ| = √(15²+20²) = √625 = 25 km (2 s.f.). For the bearing: tanθ = 15/20 = 0.75, θ = 36.87°. Bearing of Y from Z = 90° + 36.87° ≈ 127° (nearest degree).
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