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Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #24 #, how long are the other two sides?

Answer 1

Wyatt Anderson

Other two parallel sides are #color(red)(2.1648)# long

Given #A_p = 24, b = 12, theta = (3pi)/8#

To find ‘a’ the other two parallel sides.

Area of the parallelogram #A_p = b * h#

#h = 24 / 12 = 2#

#a = h / sin theta = 2 / sin ((3pi)/8) = 2.1648#

Other two parallel sides are 2.1648 long

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Answer 2

Caroline Aucoin

To find the length of the other two sides of the parallelogram, you can use the formula for the area of a parallelogram, which is base times height. The given area is 24, and one side length is 12. Thus, you can solve for the height. Once you find the height, you can use trigonometric ratios to find the lengths of the other two sides, given the angle (3π)/8. After calculating, the lengths of the other two sides are approximately 6.93.

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Answer from HIX Tutor

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