The Sine Rule · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Pair the side with its angle

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. In triangle ABC, angle A is 30 degrees with opposite side a of 4 cm. Angle B is 90 degrees. Use the sine rule to find side b in cm.

    Answer: ______________

  2. What must you pair up before substituting into the sine rule?

    • The two longest sides together
    • All three angles with each other
    • Each side with the angle opposite it

  3. Angle A is 30 degrees with opposite side 4 cm, and angle B is 90 degrees. Use the sine rule to find side b, in cm.

    Answer: ______________

  4. When is the sine rule the right tool?

    • A side and its opposite angle are both known
    • Two sides and the included angle are known
    • All three sides are known

  5. A sine rule calculation gives a missing angle of 30 degrees on your calculator, but the triangle diagram shows an obtuse angle. What should you do?

    • Also test 150 degrees, because sin 150 equals sin 30
    • Keep 30 degrees, because calculators are always right
    • Switch to the cosine rule instead
    • Measure the angle with a protractor

  6. Side a is 7 cm opposite angle A of 30 degrees, and side b is 14 cm. Use the sine rule to find angle B, in degrees.

    Answer: ______________

  7. Angle A is 30 degrees with opposite side 6 cm, and angle B is 90 degrees. Find side b, in cm, using the sine rule.

    Answer: ______________

  8. Angle A is 30 degrees with opposite side 6 cm, and angle B is 90 degrees. Find side b in cm using the sine rule.

    Answer: ______________

  9. You know two sides and the angle trapped between them, but no opposite pair. Which rule fits?

    • The sine rule
    • The cosine rule
    • Pythagoras, whatever the angle

  10. Side a is 7 cm opposite angle A of 30 degrees, and side b is 14 cm. What is angle B?

    • 90 degrees
    • 30 degrees
    • 60 degrees
    • 45 degrees
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Pair the side with its angle W1-mt_cTt_-9KZho-s1

  1. 8 · Pair side a with angle A, then b = 4 x sin 90 / sin 30 = 4 / 0.5 = 8.
  2. Each side with the angle opposite it · The rule links each side to the sine of its opposite angle.
  3. 8 · b equals 4 times sin 90 over sin 30, which is 4 over 0.5.
  4. A side and its opposite angle are both known · One full side-angle pair starts the rule; without it you switch tools.
  5. Also test 150 degrees, because sin 150 equals sin 30 · Sine is shared by supplementary angles, so 30 and 150 both fit the equation and the diagram decides.
  6. 90 · Sin B equals 14 times 0.5 over 7, which is 1, so B is 90 degrees.
  7. 12 · b equals 6 over sin 30, which is 6 over 0.5.
  8. 12 · b = 6 x sin 90 / sin 30 = 6 / 0.5 = 12.
  9. The cosine rule · With no full pair the sine rule cannot start, so the cosine rule takes over.
  10. 90 degrees · sin B = 14 x 0.5 / 7 = 1, and the angle with sine 1 is 90 degrees.
Worksheet · LightMySky