Posted by samuel on Monday, April 18, 2011 at 7:59am.
The cosine rule gives the formula for the cosine of an angle when the three sides are known:
cos(A)=(B²+C²-A²)/(2BC)
where B and C are lengths of sides adjacent to A.
We know that a positive angle is acute when cos(A) is positive, which in turn requires that
B²+C²-A²>0 ....(1)
So if all three angles of a triangle have to be acute, we have the two additional requirement analogous to (1) above:
C²+A²-B²>0
A²+B²-C²>0
If the third side can be chosen such that all three conditions are satisfied, the triangle has acute angles.
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