A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Classify it as acute, obtuse, or right.

obtuse

right

acute

81^2 = 18 ^2 + 80^

6561 = 324 + 6400

6561 = 6724

It is not a right angle, since 18^2 + 80^2 does not equal 81^2.

So,

Using The law of cosines:

The largest angle C is opposite to the side c.

Therefore,

c^2 = a^2 + b^2 - 2ab cosC

Here,

c^2 < (a^2 + b^2)

cosC must be positive which makes C an acute angle.