Question

A triangle has side lengths of 18 in., 22 in., and 29 in. Is the triangle acute, obtuse, or right?

Acute
Obtuse
Right
None of the above

Answer 1

Answer: Obtuse

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Step-by-step explanation:

We have a triangle with these side lengths

• a = 18
• b = 22
• c = 29

Computing a^2+b^2 gets us

a^2+b^2 = 18^2+22^2 = 808

Compare this to c^2

c^2 = 29^2 = 841

Because 808 < 841, this means a^2+b^2 < c^2

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We have three cases:

• If a^2+b^2 > c^2, then the triangle is acute
• If a^2+b^2 = c^2, then we have a right triangle
• If a^2+b^2 < c^2, then the triangle is obtuse

For more information, check out the converse of the Pythagorean Theorem.