Calculating the length of the hypotenuse
Example
Use Pythagoras' theorem to calculate the length of the hypotenuse. Give your answer to 2 decimal places.
Write the equation: \(x^{2} = 7^{2} + 4^{2}\)
Square the lengths you know: \(x^{2} = 49 + 16\)
Add together: \(x^{2} = 65\)
Find the square root: \(x = \sqrt {65}\)
\(= 8.06\,(to\,2\,d.p.)\)
Now try these questions.
Question
\(x^{2} = 6^{2} + 10^{2}\)
\(x^{2} = 36 + 100\)
\(x^{2} = 136\)
\(x = \sqrt {136}\)
\(= 11.66\,(to\,2\,d.p.)\)
Question
\(a^{2} = 5^{2} + 11^{2}\)
\(a^{2} = 25 + 121\)
\(a^{2} = 146\)
\(a = \sqrt {146}\)
\(= 12.08\,(to\,2\,d.p.)\)
Question
\(s^{2} = 1.4^{2} + 2.5^{2}\)
\(s^{2} = 1.96 + 6.25\)
\(s^{2} = 8.21\)
\(s = \sqrt {8.21}\)
\(= 2.87\,(to\,2\,d.p.)\)
If you got these right you have successfully used Pythagoras' theorem to calculate the length of the hypotenuse.