Question

if a triangle has side length of 8, 10 and 14. Would it represent an acute, right or obtuse triangle?

Answer 1

with:

a = 8

b = 10

c = 14

Using law of cosines:

$\begin{gathered} cos(C)\text{ = }\frac{a^2+b^2\text{ - }c^2}{2ab} \\ cos(C)\text{ = }\frac{8^2+10^2\text{ - 14}^2}{2\cdot8\cdot10} \\ C\text{ = arccos(-32/160)} \\ C=101.53^{} \end{gathered}$

Then, the triangle is an obtuse triangle, because one of its angles is obtuse (greater than 90°)