Find the sides of a parallelogram where one side is 15√2, the area is 180, and one of the angles is 135 degrees.

univerkov | December 21, 2020 | education

Let the second side be equal to a.
Then the area is equal to the product of the sides and the sine of the angle between them
Since sin 135 ° = sin 45 ° = √2 / 2, then
S = a * 15√2 * (√2 / 2) / 2 = 7.5 a
By condition S = 180
7.5 * a = 180
a = 24

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