This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Morning ♡tasha♡....🧸 — let's get this done. Question 8: Given a parallelogram with sides 8 cm and 10 cm, and the angle between them is 130^. Let the parallelogram be ABCD, with AB = 8 cm, AD = 10 cm, and DAB = 130^. In a parallelogram, consecutive angles are supplementary, so ABC = 180^ - 130^ = 50^. a) Calculate the diagonals of the parallelogram. Step 1: Calculate the length of diagonal AC using the cosine rule in ABC. Sides are AB = 8 cm, BC = AD = 10 cm, and ABC = 50^. AC^2 = AB^2 + BC^2 - 2(AB)(BC)( ABC) AC^2 = 8^2 + 10^2 - 2(8)(10)(50^) AC^2 = 64 + 100 - 160(0.6428) AC^2 = 164 - 102.848 AC^2 = 61.152 AC = sqrt(61.152) ≈ 7.82 cm Step 2: Calculate the length of diagonal BD using the cosine rule in ABD. Sides are AB = 8 cm, AD = 10 cm, and DAB = 130^. BD^2 = AB^2 + AD^2 - 2(AB)(AD)( DAB) BD^2 = 8^2 + 10^2 - 2(8)(10)(130^) BD^2 = 64 + 100 - 160(-0.6428) BD^