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

folklorahhe 2021-11-29 Answered
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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Expert Answer

breisgaoyz
Answered 2021-11-30 Author has 6301 answers

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