Question
In a $\triangle\text{ABC},$ if $\angle\text{B}=\angle\text{C}=45^\circ,$ which is the longest side?
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Answer
Given that in $\triangle\text{ABC},$ 
$\angle\text{B}=\angle\text{C}=45^\circ$
We have to find longest side We know that. Sum of angles in a triangle = 180°$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{A}+45^\circ+45^\circ=180^\circ$
$\angle\text{A}=180^\circ-(45^\circ+45^\circ)=180^\circ-90^\circ=90^\circ$
$\angle\text{A}=90^\circ$
$\angle\text{B}=\angle\text{C}=45^\circ$We have to find longest side We know that. Sum of angles in a triangle = 180°$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{A}+45^\circ+45^\circ=180^\circ$
$\angle\text{A}=180^\circ-(45^\circ+45^\circ)=180^\circ-90^\circ=90^\circ$
$\angle\text{A}=90^\circ$
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