Question

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

Answer 1

the angle maybe 90 degrees in my view

Answer 2

Answer:

Can not determined.

Step-by-step explanation:

Since, the opposite angle of the largest side in the triangle is always largest,

Here, the given sides of the triangle are a, 3a and √3 a

Let $\theta$ be the largest angle of the triangle,

Since, 3a is the largest side of the triangle.

By the cosine law,

$(3a)^2=a^2+(\sqrt{3}a)^2-2a(\sqrt{3}a) cos \theta$

$9a^2=a^2+3a^2-2\sqrt{3}a^2cos \theta$

$9a^2-4a^2 = -2\sqrt{3}a^2cos \theta$

$-5a^2=2\sqrt{3}a^2cos \theta$

$-5 = 2\sqrt{3}cos \theta$

$\implies cos \theta = \frac{-5}{2\sqrt{3}}\implies \theta = \text{ can not determined}$

Hence, the triangle is not possible having the given sides.