Question

Three sides of a triangle are a, 3a and 3a. Find the measurement of angle opposite to the largest side.

Answer 1

Let In △ ABC, AB = a,  BC = 3a  and AC = 10−−√ a

Now, AB2 + BC2 = a2 + (3a)2 = a2 + 9a2 = 10a2and  AC2 = (10−−√ a)2 = 10 a2Since AB2 + BC2 = AC2  then, △ ABC is a right angled △.Such that  ∠B = 90°   [By the converse of pythagoras theorem]∴ AC is the longest side of △ ABC & the angle opposite to the longest side is 90°.

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90 degree.