WAEC Further Mathematics 2024 Objective — Question 30

Question 30 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2024 Objective paper, with the correct answer and a full explanation.

30. In triangle XYZ, |XY|=10cm, |YZ|=9cm and |XZ|=7cm. If angle XZY=alpha, find the value of cos(alpha).

• A. 11/15
• B. 17/35
• C. 5/21Correct
• D. 7/32

Explanation

Applying the cosine rule with the side opposite alpha being XY=10: 10^2=9^2+7^2-2(9)(7)cos(alpha) => cos(alpha)=(100-81-49)/(-126)=-30/-126=5/21 (see diagram).

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