Geometry and measuresGCSE / IGCSE

Pythagoras - finding a shorter side

Calculate a missing shorter side in a right-angled triangle.

  • In a right-angled triangle, , where is the hypotenuse.
  • Subtract the square of the known shorter side from the square of the hypotenuse.
  • Take the positive square root: a length cannot be negative.

Example 1

Find the shorter side .

Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.

Example 2

Find the shorter side .

Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.

Remember
Use Pythagoras only when the triangle has a right angle.

Your turn

Question 1

Find the shorter side .

Check answer
Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.
Question 2

Find the shorter side .

Check answer
Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.
Question 3

Find the shorter side .

Check answer
Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.
Question 4

Find the shorter side .

Check answer
Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.
Question 5

Find the shorter side .

Check answer
Apply this to both sides.Simplify the numerical terms and collect like terms.Take the positive square root for the stated positive quantity.
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