PrerequisitesPrerequisite

Repeated use of Pythagoras

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 the squared shared length until a square root is needed.

Example 1

Find . Both triangles are right-angled at .

Take the positive square root for the stated positive quantity.

Example 2

Find . Both triangles are right-angled at .

Take the positive square root for the stated positive quantity.

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 .

Check answer
Take the positive square root for the stated positive quantity.
Question 2

Find . Both triangles are right-angled at .

Check answer
Take the positive square root for the stated positive quantity.
Question 3

Find . Both triangles are right-angled at .

Check answer
Take the positive square root for the stated positive quantity.
Question 4

Find . Both triangles are right-angled at .

Check answer
Take the positive square root for the stated positive quantity.
Question 5

Find . Both triangles are right-angled at .

Check answer
Take the positive square root for the stated positive quantity.
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