Question

In the right - angled triangle shown, cos 0 equal to?

Answer 1

In a rigth triangle:

θ

The cosine ratio is:

$\cos\theta=\frac{adjacent}{hypotenuse}$

In the triangle given, we don't know the length of the adjacent leg to θ. We can find it using the pythagorean theorem:

$hypotenuse^2=adjacent^2+opposite^2$

In this case:

hypotenuse = 13

opposite = 12

Then:

$13^2=adjacent^2+12^2$

And solve:

$\begin{gathered} adjacent^2=13^2-12^2 \\ . \\ adjacent^2=169-144 \\ . \\ adjacent=\sqrt{25} \\ . \\ adajcent=5 \end{gathered}$

Now, we can find the cosine ratio:

$\cos\theta=\frac{5}{13}$