WAEC Mathematics 2021 Theory — Question 16
Question 16 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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10(a). A cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to: (i) two significant figures, the distance between the two farms; (ii) the nearest degree, the bearing of Manu's farm from Dogbe's.
Model answer
The angle between the two bearings at the cottage = 200°−110° = 90°. (i) By Pythagoras, distance between farms = √(3²+5²)=√34 ≈ 5.8 km (2 s.f.). (ii) θ=tan⁻¹(3/5)=30.96°; bearing of Manu's farm from Dogbe's ≈ 200°+30.96° ≈ 230° (nearest degree).
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