The sides of the parallelogram are 6 cm and 8 cm, the angle between them is 45 degrees. Find the heights of the parallelogram.

Let the sides of the parallelogram be a = 6 cm and b = 8 cm, the angle between the sides is <A = 45 °. Let’s write the formulas for the parallelogram area:
s = a * b * sin (<A) = a * h1 = b * h2, where h1 is the height to side a, h2 is the height to side b.
Given that the sides a and b, and the angle A are known, we determine the area s of the parallelogram:
s = 6 * 8 * sin 45 ° = 48 * (√2) / 2 = 24 * √2 (cm ^ 2).
Determine the heights of the parallelogram h1 and h2.
h1 = s / a = 24 * √2 / 6 = 4 * √2 (cm);
h2 = s / in = 24 * √2 / 8 = 3 * √2 (cm).