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Mathematics · Grades 9–12

Sine in a right triangle

Name the angle first; opposite is the side across from that angle.

Make a worksheet

The key idea

Name the angle first; opposite is the side across from that angle.

sin θ = opposite / hypotenuse

Worked examples

In a right triangle, the side opposite θ is 165 cm and the hypotenuse is 429 cm. Find sin θ as a fraction.

165/429 = 5/13

5/13

In a right triangle, the side opposite θ is 84 cm and the hypotenuse is 140 cm. Find sin θ as a fraction.

84/140 = 3/5

3/5

Try it yourself

  1. In a right triangle, the side opposite θ is 320 cm and the hypotenuse is 680 cm. Find sin θ as a fraction.

  2. In a right triangle, the side opposite θ is 93 cm and the hypotenuse is 155 cm. Find sin θ as a fraction.

Check your understanding

Answers and marking notes
  1. 8/17

    320/680 = 8/17

  2. 3/5

    93/155 = 3/5

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.