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The document discusses properties of triangles. It contains 5 problems: 1) Deriving the condition that sinA + sinB + sinC = 3/2 for triangle ABC. The solution is A = B = π/6, C = 2π/3. 2) Deriving conditions for triangle ABC given that cos2A + 3(cos2B + cos2C) + 5/2 = 0. The solution is A = 30°, B = C = 75°. 3) Deriving the angles of triangle ABC given that C = 120°. The solution is A = 60°, B = 60°. 4) Deriving the angles of an acute triangle ABC given that sinA +

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