Three sides of a triangle are a,3a, and root 10a Find the measurement of angle opposite to the largest side - Maths - Introduction to Trigonometry

Question

Three sides of a triangle are a,3a, and root 10a Find the
measurement of angle opposite to the largest side

Manbar Singh · Accepted Answer

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

Now, AB2 + BC2 = a2 + 3a2 = a2 + 9a2 = 10a2and  AC2 = 10 a2 = 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°

Three sides of a triangle are a,3a, and root 10a.Find the measurement of angle opposite to the largest side