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  • In a triangle, angle opposite the longest side is greater than Option: 1 <img alt="60^o" src="https://learn.careers360.com/latex-image/?60%5Eo"

In a triangle, angle opposite the longest side is greater than 

Option: 1

60^o


Option: 2

\frac{2}{3} of a right angle.


Option: 3

Can not be determined


Option: 4

Both (a) and (b)


Answers (1)

\\\text{Let AB be the longest side. Then,} \\\\ A B>B C \text { and } A B>C A \\ \\\Rightarrow \quad & \angle C>\angle A \text { and } \angle C>\angle B \\ \\ \because\text{ angle opposite to longer side is larger} \\\\ \Rightarrow \quad 2 \angle C>(\angle A+\angle B) \\\\\Rightarrow & 3 \angle C>(\angle A+\angle B+\angle C) \\ \\\Rightarrow & 3 \angle C>180^{\circ}

\\ \Rightarrow \quad \angle C>60^{\circ} \\\\ \Rightarrow \quad \angle C>\left(\frac{2}{3} \text { of a right angle }\right)

Posted by

Sumit Saini

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