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The law of cosines worksheets Grade 11

Find a side of a triangle from two sides and the angle between them.

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Free · Worked example · 14 problems · Answer key · US Letter

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How to do it

c² = a² + b² − 2ab cos C. Use it when you know two sides and the angle between them.

a =10,b=16,C=60∘:c=14\text{a }= 10, b = 16, C = 60^{\circ}:\quad c = 14
c2=a2+b2−2ab cos⁡Cc^{2} = \text{a}^{2} + b^{2} - 2\text{ab }\cos Ccos 60° = ½
102+162−2×10×16×½=19610^{2} + 16^{2} - 2 \times 10 \times 16 \times ½ = 196c² = 196
c=√196=14c = \surd 196 = 14

Example problems

  1. a =14,b=16,C=120∘:c=\text{a }= 14, b = 16, C = 120^{\circ}:\quad c =
  2. a =16,b=14,C=120∘:c=\text{a }= 16, b = 14, C = 120^{\circ}:\quad c =
  3. a =5,b=8,C=60∘:c=\text{a }= 5, b = 8, C = 60^{\circ}:\quad c =
  4. a =7,b=8,C=120∘:c=\text{a }= 7, b = 8, C = 120^{\circ}:\quad c =

Trigonometry

  1. Right triangle trigonometry: sin, cos and tan
  2. Special right triangles and exact trig values
  3. Converting degrees and radians
  4. The unit circle
  5. Amplitude and period
  6. The Pythagorean identity
  7. Simplifying trig expressions with identities
  8. Solving trigonometric equations
  9. The law of cosines
  10. The law of sines