Question

use the picture to write each ratio as a simplified fraction (how are you going to find the length of the third side?) show your thinking

Answer 1

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

$\displaystyle {a}^{2} + {b}^{2} = {c}^{2}$

$\displaystyle \implies c = \sqrt{ {a}^{2} + {b}^{2} }$

substitute:

$\displaystyle c = \sqrt{ {12}^{2} + {9}^{2} }$

simplify squares:

$\displaystyle c = \sqrt{ 225 }$

simplify square root:

$\displaystyle c = 15$

now recall that,

• $\displaystyle \sin( \theta) = \frac{opp}{hypo}$
• $\displaystyle\cos( \theta) = \frac{adj}{hypo}$
• $\displaystyle \tan( \theta) = \frac{opp}{adj}$

the ratios with respect to angle w given by

• $\displaystyle \sin( W) = \frac{12}{15} = \frac{4}{5}$
• $\displaystyle \cos(W) = \frac{9}{15} = \frac{3}{5}$
• $\displaystyle \tan( W) = \frac{12}{9} = \frac{4}{3}$

the following ratio with respect to angle X

• $\displaystyle \sin(X) = \frac{9}{15} = \frac{3}{5}$
• $\displaystyle \cos(X) = \frac{12}{15} = \frac{4}{5}$
• $\displaystyle \tan( X) = \frac{9}{12} = \frac{3}{4}$