# How do you find the sine, cosine, and tangent ratios for Angle X and Angle Y, if this triangle is a right triangle, the hypotenuse (XY) is 13 in length, the base (XZ) is 12 in length, and the leg (YZ) is 5 in length?

Oct 12, 2015

Using the definitions of the trig ratios, $\sin \theta = \frac{o p p o s i t e}{h y p o t e n u s e} , \cos \theta = \frac{a \mathrm{dj} a c e n t}{h y p o t e n u s e} , \tan \theta = \frac{o p p o s i t e}{a \mathrm{dj} a c e n t}$, we get :

#### Explanation:

From the definitions of the trig ratios we get :

$\sin X = \frac{5}{13}$
$\cos X = \frac{12}{13}$
$\tan X = \frac{5}{12}$

$S \in Y = \frac{12}{13}$
$\cos Y = \frac{5}{13}$
$\tan Y = \frac{12}{5}$