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What type of triangle has side lengths 12 , 13 , and 23–√ ?

User Svarrall
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2 votes

Answer:

obtuse

Explanation:

You want to know the type of triangle that has side lengths 12, 13, and √23.

Right triangle

Given leg lengths of √23 and 12, the Pythagorean theorem tells you the hypotenuse of a right triangle would be ...

(√23)² +12² = c²

23 + 144 = c² = 167

c = √167 ≈ 12.92

When the longest side (13) is longer than necessary for a right triangle (12.92), the largest angle is larger than 90°. The triangle is obtuse.

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Additional comment

The law of cosines can be used to find the largest angle. That relation is ...

C = arccos((a² +b² -c²)/(2ab))

C = arccos((23 +144 -169)/(2√23(12)) ≈ 91°

The largest angle is obtuse, so this is an obtuse triangle.

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User Stot
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