Choosing a Triangle Method · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Picking the right triangle rule

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

  1. You know two angles and one side of a non right angled triangle. Which method fits?

    • Sine rule
    • Cosine rule
    • Pythagoras
    • Exact trig values

  2. You know two angles and one side of a triangle. Which method fits?

    • Sine rule
    • Cosine rule
    • Pythagoras

  3. A right-angled triangle has two known sides and you need the third. Which method fits?

    • Sine rule
    • Cosine rule
    • Pythagoras

  4. You know two sides and the angle between them. Which method fits?

    • Pythagoras
    • Cosine rule
    • Sine rule

  5. A diagram splits into two right angled triangles. In the first, the hypotenuse is 10 cm and one leg is 6 cm. Work out the other leg, which is shared with the second triangle.

    Answer: ______________

  6. In the second triangle the shared 8 cm side meets a 6 cm leg at a right angle. What is the hypotenuse in cm?

    Answer: ______________

  7. Why is the cosine rule the only fit when you know two sides and the included angle?

    • A full opposite pair is known
    • No side pairs with its opposite angle
    • The triangle is right-angled

  8. Why is the cosine rule the only fit when you know two sides and the included angle?

    • The sine rule needs a side paired with its opposite angle, which you do not have
    • The sine rule only works on right angled triangles
    • The cosine rule cannot handle included angles
    • Both rules need all three sides first

  9. A triangle gives two sides and one non-included angle. Why start with the sine rule?

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

  10. A triangle gives two sides and one non-included angle. Why might you start with the sine rule?

    • A side and its opposite angle are both known
    • Two sides and the included angle are known
    • All three sides are known
    • The triangle has a right angle
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Answer key

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

Picking the right triangle rule W1-mt_nubZzZjVvn-s1

  1. Sine rule · Two angles plus one side gives a full opposite pair after the third angle, which is sine rule territory.
  2. Sine rule · The third angle completes an opposite pair, which is sine rule territory.
  3. Pythagoras · Two sides of a right-angled triangle call for Pythagoras.
  4. Cosine rule · Two sides trapping an angle with no opposite pair means cosine rule.
  5. 8 · 6-8-10 is a scaled 3-4-5 triangle, so the missing leg is 8.
  6. 10 · Root of 64 plus 36 is 10.
  7. No side pairs with its opposite angle · With no opposite pair the sine rule cannot start.
  8. The sine rule needs a side paired with its opposite angle, which you do not have · With no opposite pair available the sine rule cannot start, leaving the cosine rule as the only fit.
  9. A side and its opposite angle are both known · A known opposite pair is the fingerprint of the sine rule.
  10. A side and its opposite angle are both known · A known opposite pair is the fingerprint of the sine rule, so spotting one justifies the choice.
Worksheet · LightMySky