Answer :
Final answer:
In a triangle, the longest side is opposite the largest angle. In triangle ABC where angle A = 51 degrees, angle B = 62 degrees, and angle C = 67 degrees, the longest side will be side a, opposite the largest angle C.
Explanation:
The question involves understanding the properties of a triangle. According to the law of sines, the ratio of a triangle's side length to the sine of its opposite angle is the same for all three sides. In simpler terms, the length of a side in a triangle is proportional to the sine of the opposite angle. Therefore, the longest side will be opposite the largest angle. In the case of triangle ABC with angles A = 51 degrees, B = 62 degrees, and C = 67 degrees, the largest angle is angle C. Thus, the longest side is opposite this angle, which is side a.
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