What is the trigonometric ratio for sin C ?Enter your answer, as a simplified fraction, in the boxes.$$triangle A B C with right angle at B. B C equals 80. A C equals 82.

Answer: [tex]sin(C)=\frac{9}{41}[/tex]Step-by-step explanation:see the attached figure to better understand the problemIn the right triangle ABCFind the measure of side AB applying the Pythagoras Theorem[tex]AB^{2}=AC^{2} -BC^{2}[/tex]substitute the values[tex]AB^{2}=82^{2} -80^{2}[/tex][tex]AB^{2}=324[/tex][tex]AB=18\ units[/tex]Find the sin(C)we know thatThe function sine of angle C is equal to divide the opposite side angle C by the hypotenuseso[tex]sin(C)=\frac{AB}{AC}[/tex]substitute the values [tex]sin(C)=\frac{18}{82}[/tex]Simplify [tex]sin(C)=\frac{9}{41}[/tex]