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 triangle, and you want another side. Which method fits?

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

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

    • Sine rule
    • Cosine rule
    • Pythagoras

  3. A right-angled triangle has two known sides and you want the third. Which is the most direct method?

    • Sine rule
    • Cosine rule
    • Pythagoras

  4. You know two sides of a non right angled triangle and the angle between them, and you want the third side. Which method fits?

    • Pythagoras
    • Cosine rule
    • Sine rule

  5. A diagram splits into two right angled triangles. The first has hypotenuse 10 cm and one leg 6 cm. What is the other leg, shared with the second triangle, in cm?

    Answer: ______________

  6. A right-angled triangle has legs of 8 cm and 6 cm. What is the hypotenuse, in cm?

    Answer: ______________

  7. Which method is the most direct for finding the third side of a non right angled triangle when you know two sides and the included angle?

    • Sine rule, since it works on every triangle
    • Cosine rule, as no opposite pair is available
    • Pythagoras, since every triangle reduces to it in the end

  8. Why is the cosine rule the direct fit for the third side when you know two sides and the included angle of a non right angled triangle?

    • The sine rule only works on right angled triangles, never otherwise
    • The sine rule needs an opposite pair, which you do not have
    • 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, with the angle opposite one of the sides. 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, with the angle opposite one of the sides. Why might you start with the sine rule?

    • Two sides and the included angle are known
    • All three sides are known
    • The triangle has a right angle
    • A side pairs with its opposite 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 starts the sine rule.
  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 · Root of 100 minus 36 is 8.
  6. 10 · Root of 64 plus 36 is 10.
  7. Cosine rule, as no opposite pair is available · With no opposite pair available the sine rule cannot start directly, so the cosine rule is the most direct fit.
  8. The sine rule needs an opposite pair, which you do not have · With no opposite pair available the sine rule cannot start directly, leaving the cosine rule as the direct fit.
  9. A side and its opposite angle are both known · A known opposite pair plus another side starts the sine rule; the second side may give two triangles, so check the answer.
  10. A side pairs with its opposite angle · A side and its opposite angle are both known, and the extra side starts the rule. The second side can give two triangles, so check the answer.
Worksheet · LightMySky