Question
In $\triangle\text{ABC},\angle\text{A}=50^{\circ}$ and $\angle\text{B}=60^{\circ}$ Determine the longest and shortest sides of the triangle.
✓
Answer
Given: $\triangle\text{ABC},\angle\text{A}=50^{\circ}$ and $\angle\text{B}=60^{\circ}$ In $\triangle\text{ABC},$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$ (Angle sum property of a triangle)
$\Rightarrow50^{\circ}+60^{\circ}+\angle\text{C}=180^{\circ}$
$\Rightarrow110^{\circ}+\angle\text{C}=180^{\circ}$
$\Rightarrow\angle\text{C}=180^{\circ}-110^{\circ}$
$\Rightarrow\angle\text{C}=70^{\circ}$
Hence, the longest side will be opposite to the largest angle $\big(\angle\text{C}=70^{\circ}\big)$
i.e. $AB$. And,
the shortest side will be opposite to the smallest angle $\big(\angle\text{A}=50^{\circ}\big)$ i.e. $BC.$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$ (Angle sum property of a triangle)
$\Rightarrow50^{\circ}+60^{\circ}+\angle\text{C}=180^{\circ}$
$\Rightarrow110^{\circ}+\angle\text{C}=180^{\circ}$
$\Rightarrow\angle\text{C}=180^{\circ}-110^{\circ}$
$\Rightarrow\angle\text{C}=70^{\circ}$
Hence, the longest side will be opposite to the largest angle $\big(\angle\text{C}=70^{\circ}\big)$
i.e. $AB$. And,
the shortest side will be opposite to the smallest angle $\big(\angle\text{A}=50^{\circ}\big)$ i.e. $BC.$
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