The sides of the parallelogram are 3 and 8 cm, and one of the corners of the parallelogram is 60 °. Find the large diagonal of the parallelogram.
The large diagonal of the parallelogram lies against its larger angle.
The sum of the adjacent angles of the parallelogram is 180, then the angle ABC = 180 – BAD = 180 – 60 = 120.
For triangle ABC, apply the cosine theorem.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = 9 + 64 – 2 * 3 * 8 * (-1/2) = 73 + 24 = 97.
AC = √97 cm.
Answer: The length of the larger diagonal is √97 cm.
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