Given a rhombus, the smaller diagonal is 18, and the side is 15. Find the cos of the smaller angle.

The smaller corner of the rhombus lies opposite its smaller diagonal. This diagonal and the two sides of the rhombus form a triangle. By the cosine theorem:

a² = b² + c² – 2bc * cos α, where b and c are the sides of the rhombus, a is its smaller diagonal, α is the angle between the sides of the rhombus.

From this formula, we express the cosine:

cos α = (b² + c² – a²) / (2bc).

Find the cosine of the angle:

cos α = (15² + 15² – 18²) / (2 * 15 * 15) = (225 + 225 – 324) / 450 = 126/450 = 0.28.

Answer: The cosine of the smaller angle of the rhombus is 0.28.

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