Posted by **Cindy** on Wednesday, December 14, 2011 at 9:25pm.

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

- geometry -
**drwls**, Thursday, December 15, 2011 at 6:28am
With two long, almost equal, sides and a short side, you can visualize it in your head. It is acute.

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

The law of cosines can be used to answer the problem numerically.

The largest angle C is opposite the longest side, c.

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

When c^2 < (a^2 + b^2), as it is here, cosC must be positive, making C an acute angle.

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