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