# M18

Question: Below is a right-angled triangle. Work out the length of the side marked $x$. Give your answer to two decimal places.

Answer: To do this we will need to use Pythagoras theorem $a^2+b^2=c^2$

We then add the numbers we know into the equation. This gives us

$9^2+x^2=13^2$

Next, we need to rearrange to make $x$ the subject.

$x^2=13^2 - 9^2$

Next if we then calculate the right-hand side:

$x^2=169 - 81$

$x^2=88$

Finally, we square root both sides

$x=9.38$

Which gives the final answer to be $x=9.38$ (2d.p.)