Answer:
See below
Step-by-step explanation:
to figure out the ratios we must figure out the length of hypotenuse first to do so we can consider Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] \displaystyle \implies c = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
substitute:
[tex] \displaystyle c = \sqrt{ {12}^{2} + {9}^{2} } [/tex]
simplify squares:
[tex] \displaystyle c = \sqrt{ 225 } [/tex]
simplify square root:
[tex] \displaystyle c = 15[/tex]
now recall that,
- [tex] \displaystyle \sin( \theta) = \frac{opp}{hypo} [/tex]
- [tex] \displaystyle\cos( \theta) = \frac{adj}{hypo} [/tex]
- [tex] \displaystyle \tan( \theta) = \frac{opp}{adj} [/tex]
the ratios with respect to angle w given by
- [tex] \displaystyle \sin( W) = \frac{12}{15} = \frac{4}{5} [/tex]
- [tex] \displaystyle \cos(W) = \frac{9}{15} = \frac{3}{5} [/tex]
- [tex] \displaystyle \tan( W) = \frac{12}{9} = \frac{4}{3} [/tex]
the following ratio with respect to angle X
- [tex] \displaystyle \sin(X) = \frac{9}{15} = \frac{3}{5} [/tex]
- [tex] \displaystyle \cos(X) = \frac{12}{15} = \frac{4}{5} [/tex]
- [tex] \displaystyle \tan( X) = \frac{9}{12} = \frac{3}{4} [/tex]
