Using the hypotenuse to find another side
Pythagoras’ theorem can also be used to find the length of another side of a triangle using the hypotenuse.
The square on the hypotenuse subtracted by the square on another side is equal to the square on the remaining side.
To find this, we have rearranged the original formula \({a}{^2}~{=}~{b}{^2}~{+}~{c}{^2}\) to find:
\({b}{^2}~{=}~{a}{^2}~{-}~{c}{^2}\)
\({c}{^2}~{=}~{a}{^2}~{-}~{b}{^2}\)
Find the length of AB, giving your answer to two decimal places.
In this triangle, we know the hypotenuse so we will need to subtract from the hypotenuse.
AB2 = 122 – 52
AB2 = 144 – 25
AB2 = 119
AB = \(\sqrt{119}\)
AB = 10.90871211
AB = 10.91 mm (to two decimal places)
Question
Find the length of the side marked \({z}\).
Round your answer to two decimal places.
\({z}{^2}\) = 422 – 352
\({z}{^2}\) = 1,764 – 1,225
\({z}{^2}\) = 539
\({z}\) = \(\sqrt{539}\)
\({z}\) = 23.21637353
\({z}\) = 23.22 m (to two decimal places)
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