# Trigonometry

The common three trigonometric ratios are sine, cosine and tangent which are defined by the following triangle:

abc show us the sides, ABC represent the angles.

$Sine\, of\, A=\frac{measure\,of\,the\,leg\,opposite\,angle\,A}{measure\,of\,the\,hypotenuse}$

$\Rightarrow sin\left ( A \right )=\frac{a}{c}$

$Cosine\,of\,A=\frac{measure\,of\,the\,leg\,adjacent\,to\, angle\,A}{measure\,of\,the\,hypotenuse}$

$\Rightarrow cos\left ( A \right )=\frac{b}{c}$

$Tangent\, of\, A=\frac{measure\,of\,the\,leg\,opposite\,angle\,A}{measure\,of\,the\,leg\,adjacent\,to\,angle\,A}$

$\Rightarrow tan\left ( A \right )=\frac{a}{b}$

Example

Find the sin(B), cos(B) and tan(B).

$Sine\, of\, B=\frac{measure\,of\,the\,leg\,opposite\,angle\,B}{measure\,of\,the\,hypotenuse}$

$Sin\, B=\frac{9}{15}=\frac{3}{5}=0.6$

$Cosine\,of\,B=\frac{measure\,of\,the\,leg\,adjacent\,to\, angle\,B}{measure\,of\,the\,hypotenuse}$

$Cos\, B=\frac{6}{15}=\frac{2}{5}=0.4$

$Tangent\, of\, B=\frac{measure\,of\,the\,leg\,opposite\,angle\,B}{measure\,of\,the\,leg\,adjacent\,to\,angle\,B}$

$Tan\, B=\frac{9}{6}=1.5$

## Video lesson

Find the measure of angle a in this right triangle