Posted by **Matthew** on Sunday, May 2, 2010 at 9:20pm.

Classify the triangle as right, acute, or obtuse if the measures of its sides are 28, 46, and 53.

- geometry -
**MathMate**, Sunday, May 2, 2010 at 9:43pm
Use the cosine rule:

cos(A)=(b²+c²-a²)/(2bc)

When a is the hypotenuse of a right-triangle, cos(A)=0.

When a<90° cos(A)>0

When a>90° cos(A)<0

So by evaluating the cosine opposite the longest side, you can tell if the triangle is a right-triangle, acute or obtuse.

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