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△ Trigonometry

Law of Cosines

Find a side when two sides and included angle known

Formula

c² = a² + b² − 2ab cos C

Find a side when two sides and included angle known

Example

  • a=5, b=7, C=60°
  • c² = 25+49−70×0.5 = 39
  • c ≈ 6.24
Result ≈ 6.24
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Grade 10 Law of Cosines

Grade 10 · Law of Cosines

Easy 20 questions Worksheet #79694 For Law of Cosines

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MathDigits Worksheet

Grade 10 · Law of Cosines

Easy · 20 questions · Worksheet #79694 · Law of Cosines

Name: ________________________

Date: ______________ Score: ______

  1. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  2. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  3. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  4. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  5. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  6. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  7. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  8. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  9. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  10. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  11. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  12. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  13. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  14. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  15. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  16. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  17. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  18. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  19. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________
  20. fill Law of Cosines: a = 5, b = 7, C = 60°. Find side c. (c² = a²+b²−2ab cos C, cos60°=0.5)
    ______________________________

Updated July 2026

FAQs

What is Law of Cosines?

Law of Cosines (law of cosines) is a trigonometry relationship written as Find a side when two sides and included angle known or c² = a² + b² − 2ab cos C. Students use it to solve unknowns when enough values are known.

How do you calculate Law of Cosines step by step?

Write Find a side when two sides and included angle known, substitute the known numbers carefully, then simplify. Worked walkthrough: a=5, b=7, C=60° c² = 25+49−70×0.5 = 39 c ≈ 6.24.

When is Law of Cosines taught in school?

Law of Cosines usually appears in trigonometry units during middle or secondary school. Match difficulty with MathDigits grade worksheets so practice fits the curriculum year.

What is a real example of Law of Cosines?

On this page the worked result is ≈ 6.24. Generate a formula worksheet below for more unique practice sets.

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