The length of the diagonal d is 17 in if the lengths of the sides of the parallelogram are 6 in and 12 in.
What is parallelogram?
In two-dimensional geometry, it is a plane shape having four sides in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
We know the law of cosine to find the diagonal length d:
[tex]\rm d^2 = AD^2+AB^2-2AD\timesAB \times CosA[/tex]
We have AD = 6 in
AB = 12 in
∠A = 130°
Put these values in the above formula:
[tex]\rm d^2 = 6^2+12^2-2\times6\times12 \times Cos130\\[/tex]
d² = 36+144-(144Cos130)
d = √272.56
d = 16.50 in ≈ 17 in (nearest to inches)
Thus, the length of the diagonal d is 17 in if the lengths of the sides of the parallelogram are 6 in and 12 in.
Learn more about the parallelogram here:
brainly.com/question/1563728
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