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

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    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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