Given:
• Hypotenuse = 13
,• Length of longer leg = 12
,• Length of shorter leg = 5
Let's determine the relationship of the ratios of sin(x) and cos(y).
For sin(x), apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse}}[/tex]Where:
θ is the angle = x
opposite side is the side opposite the angle = 12
Hypotenuse is the longest side of the triangle = 13
Thus, we have:
[tex]sinx=\frac{12}{13}[/tex]• For cos y:
Apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{\text{ adjacent }}{hypotenuse}[/tex]Where:
θ is the angle = y
Adjacent side is the side adjacent the angle = 12
Hypotenuse = 13
Thus, we have:
[tex]\text{ cos}y=\frac{12}{13}[/tex]Therefore, we can see that the ratios are the same:
[tex]\begin{gathered} sinx=\frac{12}{13} \\ \\ cosy=\frac{12}{13} \end{gathered}[/tex]ANSWER:
[tex]\text{ The ratios are identical \lparen}\frac{12}{13}\text{ and }\frac{12}{13})[/tex]