Geometry and trigonometryAI HL

Finding a side using trigonometry

Choose sine, cosine or tangent from the known and unknown sides.

  • Label the sides relative to the chosen acute angle.
  • Choose a ratio containing both the known and unknown sides, then rearrange.
RatioSides
Opposite and hypotenuse
Adjacent and hypotenuse
Opposite and adjacent

Example 1

Find the opposite . 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.

Example 3

Find the opposite . 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.

Remember
Use degree mode and round only the final answer.

Your turn

Question 1

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 2

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 3

Find the adjacent . 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 4

Find the opposite . 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 5

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.
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