Trigonometry ratios are used to show the relationship between the sides of a right-angled triangle.
The trigonometry ratios are [tex]\mathbf{sin \ R= \frac{12}{13}}[/tex], [tex]\mathbf{sin \ S= \frac{5}{13}}[/tex], [tex]\mathbf{cos \ R= \frac{5}{13}}[/tex], [tex]\mathbf{cos\ S= \frac{12}{13}}[/tex], [tex]\mathbf{tan\ R= \frac{12}{5}}[/tex], [tex]\mathbf{tan\ S= \frac{5}{12}}[/tex]
The given parameters (see attachment) are:
[tex]\mathbf{RS = 13}[/tex]
[tex]\mathbf{ST = 12}[/tex]
[tex]\mathbf{RT = 5}[/tex]
The trigonometry ratios are calculated using:
[tex]\mathbf{sin \theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{cos \theta = \frac{Adjacent}{Hypotenuse}}[/tex]
[tex]\mathbf{tan \theta = \frac{Opposite}{Adjacent}}[/tex]
So, we have:
[tex]\mathbf{sin \ R= \frac{12}{13}}[/tex]
[tex]\mathbf{sin \ S= \frac{5}{13}}[/tex]
[tex]\mathbf{cos \ R= \frac{5}{13}}[/tex]
[tex]\mathbf{cos\ S= \frac{12}{13}}[/tex]
[tex]\mathbf{tan\ R= \frac{12}{5}}[/tex]
[tex]\mathbf{tan\ S= \frac{5}{12}}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
