# Triangles ABC and DEF are right triangles, as shown. \triangle

Triangles ABC and DEF are right triangles, as shown. $$\displaystyle\triangle{A}{B}{C}$$ is similar to $$\displaystyle\triangle{D}{E}{F}$$.
Which ratios are equal to $$\displaystyle{\cos{{\left({B}\right)}}}$$ ? Choose the TWO ratios that apply.

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Step 1
Solytion-Given thet $$\triangle ABC$$ and $$\displaystyle\triangle{D}{E}{F}$$ avenight tnangle and $$\displaystyle\triangle{A}{B}{C}\approx\approx{D}{E}{F}$$
Now as we know
$$\displaystyle{\cos{\theta}}={\frac{{{B}{a}{s}{e}}}{{Hyotenuse}}}$$
2)$$\displaystyle{\cos{{B}}}={\frac{{{B}{C}}}{{{A}{B}}}}-{1}$$
Step 2
Now by similanty vation pvoperty we know
$$\displaystyle{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{F}}}}$$
$$\displaystyle\Rightarrow{\frac{{{E}{F}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{A}{B}}}}-{\left({2}\right)}$$
from (1)and (2)
$$\displaystyle{\cos{{B}}}={\frac{{{E}{F}}}{{{D}{E}}}}$$