Suppose we are given the equation of the sides of a triangle, how can we determine whether the triangle is obtuse angled or acute angled? In case of a right angled triangle, I would simply check whether the slopes $m_1$ and $m_2$ of any two lines follow the relation $m_1m_2=-1$. I know to find the angle between two intersecting lines with slopes $m_1$ and $m_2$ using the following formula:
$$\tan \theta = \left|\frac{m_2-m_1}{1+m_1m_2} \right|$$
The problem is, the above formula is helpful in finding only the positive values of the tangent function, or only for acute angles, due to the presence of the absolute value function.
Are there any other algorithm to distinguish acute angle triangles from obtuse angled triangles? Is it possible to use the same formula to find them?
Best Answer
Hint: calculate $$a^2+b^2-c^2,a^2+c^2-b^2,b^2+c^2-a^2$$