# In right triangle ABC, with right angle C, AB = 9, and BC = 5, how do you find the length of the missing side?

Aug 11, 2015

color(blue)(CA=2sqrt14

#### Explanation:

In a right angled triangle, right angled at C, the hypotenuse = $A B$

As the triangle is a right angled triangle, the Pythagoras Theorem can be applied to find the unknown side.

As per the Pythagoras Theorem:

color(green)((AB)^2 = (BC)^2 +(CA)^2

$A B = 9 , B C = 5$

So,
${9}^{2} = {5}^{2} + C {A}^{2}$

$81 = 25 + C {A}^{2}$

$C {A}^{2} = 56$

$C A = \sqrt{56}$

color(blue)(CA=2sqrt14