In a triangle, the lengths of the sides are consecutive integers, and the largest is twice as large as the smallest. Determine the cosine of the smallest angle.

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In a triangle, the lengths of the sides are consecutive integers, and the largest is twice as large as the smallest. Determine the cosine of the smallest angle.
The sides of the triangle are 2, 3, and 4 units long. These numbers satisfy the triangle inequality, so such a triangle exists. We are looking for the cosine of the angle opposite the smallest side, its value is $\frac{7}{8}$.