Video: Solving for the Hypotenuse of a Right Triangle

Find π‘₯ in the right triangle shown.


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 Pythagoras’s theorem. This states that π‘Ž squared plus 𝑏 squared equals 𝑐 squared. Well, length 𝑐 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 𝐴𝐡 in the right triangle is π‘₯ equals five.

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