Geometry and measuresKey Stage 3

Finding a length with the cosine ratio

Choose the known and unknown sides, then rearrange the cosine ratio.

  • Label sides relative to the angle: is opposite, is adjacent, is the hypotenuse.
  • Use . The hypotenuse is always opposite the right angle.
  • Use degree mode. Round only the final length.

Example 1

Find the adjacent . Give your answer to 1 decimal place.

Apply this to both sides; then write the subject on the left.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.

Example 2

Find the hypotenuse . Give your answer to 1 decimal place.

Apply this to both sides.Apply this to both sides.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.

Remember
Choose sine for opposite and hypotenuse, cosine for adjacent and hypotenuse, or tangent for opposite and adjacent.

Your turn

Question 1

Find the adjacent . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.
Question 2

Find the hypotenuse . Give your answer to 1 decimal place.

Check answer
Apply this to both sides.Apply this to both sides.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.
Question 3

Find the adjacent . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.
Question 4

Find the hypotenuse . Give your answer to 1 decimal place.

Check answer
Apply this to both sides.Apply this to both sides.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.
Question 5

Find the adjacent . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.Evaluate in degree mode and keep the full calculator value.Keep the full value until the final step.To 1 decimal place.
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