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

August 22, 2021 | education

| 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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