Question 784764: Hello, in preparation for the quantitative portion of the GRE i came upon this question. In triangle ABC, < A is 62 degrees, < B is 58 degrees. It then asks if If quantity AB or AC is greater. I know that angle AC is 62 degrees, so I answered that quantity AC is greater than AB. It stated that AB is greater becase < C is greater than < B. How am I incorrect on this?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If angle A is 62 and angle B is 58, then, because the sum of the angles of a triangle is 180 degrees, angle C has to be 60 degrees. Assuming a scalene triangle (which this is), the side of a triangle opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side. Since angle B is the smallest of the three angles, the side opposite angle B, namely the segement AC, must be the shortest side. In that AC is the shortest side it must be shorter than any other side, hence AB is longer than AC.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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