Triangles ABC and DEF are right triangles, as shown \triangle ABC is simil

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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Solution: Given that $$\displaystyle\triangle{A}{B}{C}$$ and $$\displaystyle\triangle{D}{E}{F}$$ are right triangle and $$\displaystyle\triangle{A}{B}{C}\approx\triangle{D}{E}{F}$$
Now as we know
$$\displaystyle{\cos{\theta}}={\frac{{{B}{a}{s}{e}}}{{{H}{y}{p}{o}{tan{{c}}}{o}{u}{s}}}}$$
$$\displaystyle{\cos{{B}}}={\frac{{{B}{C}}}{{{A}{B}}}}$$
Step 2
Now by similarity ratio property we know
$$\displaystyle{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{F}}}}$$
$$\displaystyle\Rightarrow{\frac{{{E}{F}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{A}{B}}}}$$
from (1) and (2)
$$\displaystyle{\cos{{B}}}={\frac{{{E}{F}}}{{{D}{E}}}}$$