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

podnescijy 2021-11-17 Answered
Triangles ABC and DEF are right triangles, as shown \(\displaystyle\triangle{A}{B}{C}\) is similar to \(\displaystyle\triangle{D}{E}{F}\)
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Which ratios are equal to \(\displaystyle{\cos{{\left({B}\right)}}}\)? Choose the TWO ratios that apply.

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Expert Answer

Donald Proulx
Answered 2021-11-18 Author has 1698 answers

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)
\(\displaystyle{\cos{{B}}}={\frac{{{E}{F}}}{{{D}{E}}}}\)

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