Question

three sides of a triangle are a,3a,√3a.find the measurement of angle opposite to the largest side

Answer 1

Three sides of triangle are ; a , 3a , √3a

Let ABC is a triangle.

and Let us consider that, AB = a , BC = 3a and CA = √3a

here, BC = 3a is largest side of triangle.

so, we have to find angle opposite to the largest side , BC e.g., $\angle A$

use cosine formula to find angle of triangle.

$cosA=\frac{b^2+c^2-a^2}{2bc}$

or, $cosA=\frac{AB^2+CA^2-BC^2}{2AB.CA}$

or, $cosA=\frac{a^2+3a^2-9a^2}{2.a.\sqrt{3}a}$

or, $cosA=\frac{-5a^2}{2\sqrt{3}a^2}$

or, $cosA\neq\frac{-5}{2\sqrt{3}}$ actually, this is happened because a, 3a and √3a are not sides of any triangle.

from rule of triangle, sum of two sides of triangle must be greater than 3rd side.

but a + √3a < 3a ,

so, this is incorrect that, a , 3a and √3a are sides of triangle.