Re: Lengths of three sides of a triangle are 5, 6 and 8. Degree measure
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13 Feb 2025, 13:36
Let the three sides of the triangle be $\(\mathrm{AB}=5, \mathrm{BC}=6 \& \mathrm{AC}=8\)$
We have $\(5^2+6^2=25+36=41<8^2=64\)$, so angle ABC must be greater than 90 degrees.
[Note:- In a triangle say $\(\mathrm{ABC}, \mathrm{AC}^2=\mathrm{AB}^2+\mathrm{BC}^2 \Leftrightarrow \angle \mathrm{~B}=90^{\circ}, \mathrm{AC}^2>\mathrm{AB}^2+\mathrm{BC}^2 \Leftrightarrow \angle \mathrm{~B}>90^{\circ}\)$ $\(\left.\& \mathrm{AC}^2<\mathrm{AB}^2+\mathrm{BC}^2 \Leftrightarrow \angle \mathrm{~B}<90^{\circ}\right]\)$
So, the sum of the remaining two angles of triangle i.e. $\(\angle \mathrm{BAC}+\angle \mathrm{ACB}=\mathrm{x}+\mathrm{y}\)$ must be less than 90 degrees (Sum of the angles of a triangle is 180 degrees).
Hence column B has higher quantity when compared with column A, so the answer is (B).