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15 December, 02:53

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length a is acute. What must be true?

A. b^2 + c^2 < a^2

B. a^2 + b^2 = c^2

C. a^2 + b^2 > c^2

D. b^2 + c^2 > a^2

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  1. 15 December, 03:17
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    3pi/7 < pi/2 because 3/7 < 1/2, and pi/2 is a right angle. Conclusion: the angle opposite side a is an acute angle. In this situation the triangle could be a right triangle, in which case C would be true, but it does not have to be a right triangle, so don't choose C. Similarly, it could be an acute triangle, in which case B would be true, but it does not have to be, so don't choose B. Also, A says the angle opposite side a is obtuse, which is false. So don't choose A. That leaves D, which says the angle opposite side a is acute, which we know is true. So the answer is D. b^2 + c^2 > a^2
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