Kenneth ChengMathematical modeling
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In acute triangle ABC, AB=8, AC=7 and sin C=4√3/7. Find BC.

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TOPIC 01

2024 JM01

The acute-angle condition selects the positive cosine.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

In acute triangle ABC, AB=8, AC=7 and sin C=4√3/7. Find BC.

Official paper · jm01-2024 · I.10 · PDF 3

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A66
  2. Option B1212
  3. Option C22
  4. Option D33
  5. Option E55

Working and explanation

BUILD THE REASONING

Hint 1
C is acute, so cos C is positive.
Hint 2
Apply the cosine rule opposite AB.
Worked solution

  1. Find the cosine.

    cos⁡C=1−48/49=1/7\cos C=\sqrt{1-48/49}=1/7

  2. Let a=BC>0 and solve.

    64=a2+49−2(7)a(1/7)  ⟹  (a−5)(a+3)=0  ⟹  a=564=a^2+49-2(7)a(1/7)\implies(a-5)(a+3)=0\implies a=5

E: 5.

Checks and common pitfalls: The acute-angle condition selects the positive cosine.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Find the cosine.
    cos⁡C=1−48/49=1/7\cos C=\sqrt{1-48/49}=1/7
  • Let a=BC>0 and solve.
    64=a2+49−2(7)a(1/7)  ⟹  (a−5)(a+3)=0  ⟹  a=564=a^2+49-2(7)a(1/7)\implies(a-5)(a+3)=0\implies a=5

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