Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #26 #, how long are the other two sides?

Given that two opposite sides of the parallelogram have a length of 9 and the area of the parallelogram is 26, we can use the formula for the area of a parallelogram: Area = base * height. Since the base is one of the sides of length 9, we can denote it as 9. Let the other side, which is perpendicular to the given base, be denoted as h.

We know that the area is also given by the formula: Area = side * side * sin(angle), where the angle is the angle between the two sides. We can rearrange this formula to solve for the height h: h = (Area) / (9 * sin(angle)).

Substituting the given values, we have: h = 26 / (9 * sin((3pi)/8)).

After calculating this expression, we find the value of h. Then, using the Pythagorean theorem, we can find the length of the other side of the parallelogram. Let's denote this side as x.

Applying the Pythagorean theorem, we have: x^2 = h^2 + 9^2.

After finding the value of x, we will have determined the lengths of the other two sides of the parallelogram.