# Video: Solving for the Hypotenuse of a Right Triangle

Find π₯ in the right triangle shown.

01:15

### Video Transcript

Find π₯ in the right triangle shown.

In order to calculate a missing length in a right-angled triangle, we need to use Pythagorasβs theorem. This states that π squared plus π squared equals π squared. Well, length π is the hypotenuse or longest side of the triangle. This will always be found opposite the right angle. In this question, the hypotenuse is π₯.

Substituting in the values from the triangle gives us an equation four squared plus three squared equals π₯ squared. Four squared is equal to 16 and three squared is equal to nine. Therefore, 16 plus nine must be equal to π₯ squared. 16 plus nine is 25. Therefore, π₯ squared is equal to 25.

Square rooting both sides of this equation gives us π₯ equals five, as the square root of 25 is five and the square root of π₯ squared is π₯. This means that the missing length π΄π΅ in the right triangle is π₯ equals five.