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WAEC Mathematics 2023 Theory — Question 10

Question 10 of 13 from the West African Examinations Council (WAEC) Mathematics 2023 Theory paper, with the correct answer and a full explanation.

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10(i). In a town, Chief X resides 60 m away on a bearing of 057° from the palace, P, while Chief Y resides on a bearing of 150° from the same palace, P. The residence of X and Y are 180 m apart. (a) Illustrate the information in a diagram. (b) Find, correct to three significant figures, the: (i) bearing of X from Y; (ii) distance between P and Y.

Model answer

(a) The diagram shows P at the palace, with X at 60m on bearing 057° from P, and Y at bearing 150° from P, with |XY|=180m. (b) The angle XPY=150°-57°=93°. Using the sine rule: sinθ/60=sin93°/180 → θ=sin⁻¹(60sin93°/180)≈19.44°. (i) Bearing of X from Y=270°+60°+19.44°=349° (approx, using the geometric relationships in the diagram). (ii) Using the sine rule again: |PY|/sin(67.56°)=180/sin93° → |PY|=180sin67.56°/sin93°≈167 m.

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