Calculating the length of one of the shorter sides
To calculate the length of one of the shorter sides, substitute any lengths into the Pythagoras's theorem applies to right-angled triangles. The area of the square drawn on the hypotenuse is equal to the sum of the squares drawn on the other two sides. formula and then rearrange to make \(a^2\) or \(b^2\) the subject.
Then take the square root to calculate the length of \(a\) or \(b\).
Example
Calculate the length \(a\).
\(c^2 = a^2 + b^2\)
\(10^2 = a^2 + 8^2\)
\(100 = a^2 + 64\)
Subtract 64 from both sides to make \(a^2\) the subject:
\(100 - 64 = a^2\)
\(36 = a^2\)
\(a = \sqrt{36}\)
\(a = 6~\text{cm}\)
Question
Calculate the length \(b\). Give the answer to one decimal place.
\(c^2 = a^2 + b^2\)
\((\sqrt{17})^2 = 3^2 + b^2\)
\(17 = 9 + b^2\)
Subtract 9 from both sides to make \(b^2\) the subject:
\(17 - 9 = b^2\)
\(8 = b^2\)
\(b = \sqrt{8}\)
\(b = 2.8~\text{cm}\)