Calculating the length of a shorter side
How can we use Pythagoras' theorem to calculate the length of one of the shorter sides?
Example
Calculate the length of the side marked \(a\).
Give your answer to 2 decimal places.
Write the equation: \(12^{2} = a^{2} + 8^{2}\)
Rearrange the equation: \(a^{2} = 12^{2} - 8^{2}\)
Square the lengths you know: \(a^{2} = 144 - 64\)
Do the subtraction: \(a^{2} = 80\)
Find the square root: \(a = \sqrt {80} \)
\(a = 8.94\,(to\,2\,d.p.)\)
Now try these questions:
Question
\(14^{2} = a^{2} + 9^{2}\) (You do not have to show this first line in your working)
\(a^{2} = 14^{2} - 9^{2}\)
\(a^{2} = 196 - 81\)
\(a^{2} = 115\)
\(a = \sqrt {115}\)
\(= 10.72\,(to\,2\,d.p.)\)
Question
\(20^{2} = r^{2} + 11^{2}\)
\(r^{2} = 20^{2} - 11^{2}\)
\(a^{2} = 400 - 121\)
\(a^{2} = 279\)
\(a = \sqrt {279}\)
\(= 16.70\,(to\,2\,d.p.)\)
Question
\(3.8^{2} = e^{2} + 2.4^{2}\)
\(e^{2} = 3.8^{2} - 2.4^{2}\)
\(a^{2} = 14.44 - 5.76\)
\(a^{2} = 8.68\)
\(a = \sqrt {8.68}\)
\(= 2.95\,(to\,2\,d.p.)\)
