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FIND THE SMALLEST ANGLE IN THE TRIANGLE! PLEASE HELP!! 25 POINTS!!

FIND THE SMALLEST ANGLE IN THE TRIANGLE! PLEASE HELP!! 25 POINTS!!-example-1
User Minimo
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2 Answers

6 votes

Answer:

Smallest Angle in the triangle is angle c.

User Kerry Jones
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5 votes

From the side/angle inequality, we see that the smallest angle of a triangle must be opposite its shortest side. In this case, that angle is opposite the shortest side
\overline{AC}, so our answer is
\boxed{\angle B}.

As for finding its measure (which I'm aware the question probably didn't ask for), we can use the law of cosines:


5^2=6^2+7^2-2(6)(7)\cos B


\cos B=(5)/(7)\implies\angle B\approx\boxed{44.4^\circ}.

User AirPett
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