Geometry and trigonometryAI HL

Repeated use of right-angled trigonometry

Find a shared side first, then use it in a second right-angled triangle.

  • Identify the two right-angled triangles and the side they share.
  • Find the shared length, then use the appropriate method again in the second triangle.
  • Keep unrounded values between steps. Round only the final answer.

Example 1

Find . Both triangles are right-angled at . Give your answer to 1 decimal place.

Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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 . Both triangles are right-angled at . Give your answer to 1 decimal place.

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

Remember
A side may be a shorter side in one triangle and the hypotenuse in another. Label each triangle separately.

Your turn

Question 1

Find . Both triangles are right-angled at . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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 . Both triangles are right-angled at . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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 . Both triangles are right-angled at . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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 . Both triangles are right-angled at . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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 . Both triangles are right-angled at . Give your answer to 1 decimal place.

Check answer
Apply this to both sides; then write the subject on the left.First find the shared side. Keep its unrounded value.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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