AI generatedGeometry and measuresGCSE Higher

Sine rule - recognising an obtuse-angle alternative

Sine rule: recognising an obtuse-angle alternative.

  • Label the sides and angles before choosing a rule.
  • Sine rule: matching opposite pairs. Cosine rule: three sides or two sides and the included angle.
  • Use degree mode. Keep full calculator accuracy until the final rounding step.

Example 1

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 36.9° or 143.1°. Both are positive and each leaves a positive third angle with A = 30°.

Example 2

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 35.7° or 144.3°. Both are positive and each leaves a positive third angle with A = 30°.

Your turn

Question 1

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 34.8° or 145.2°. Both are positive and each leaves a positive third angle with A = 30°.
Question 2

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 34.2° or 145.8°. Both are positive and each leaves a positive third angle with A = 30°.
Question 3

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 33.7° or 146.3°. Both are positive and each leaves a positive third angle with A = 30°.
Question 4

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 44.4° or 135.6°. Both are positive and each leaves a positive third angle with A = 30°.
Question 5

Find both possible values of B. Explain why both form a triangle. Give angles to 1 decimal place.

Triangle ABC; lengths in cmABCDiagram not to scale
Check answer
Use matching opposite side–angle pairs.Evaluate sin 30° = .Find the acute calculator value.First possible angle.Sine has the same value for supplementary angles.
B = 41.8° or 138.2°. Both are positive and each leaves a positive third angle with A = 30°.
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