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)

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