# Question #cb1e2

Feb 25, 2018

Given $\sin \theta = \frac{12}{13}$

We know, $\sin \theta = \left(\text{opposite side")/("hypotenuse}\right)$

Therefore, $\text{opposite side} = 12$ and $\text{hypotenuse} = 13$

so the third side, $x$ can be found by applying Pythagoras theorem.

i.e. ${\left(\text{hypotenuse")^2=("opposite side}\right)}^{2} + {x}^{2}$
${x}^{2} = {13}^{2} - {12}^{2} = 169 - 144 = 25$
$x = 5$ units.

Now, $\cos \theta = \left(\text{adjacent side")/("hypotenuse}\right)$
$\cos \theta = \frac{5}{13}$