PrerequisitesPrerequisite

The Pythagorean theorem - finding a shorter side

Calculate a missing shorter side in a right triangle.

  • In a right 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 The Pythagorean theorem 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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