Find the area of a parallelogram if its two sides are 10 and 15, and the angle between them is 60 degrees.

First way.

The area of a parallelogram is equal to the product of the lengths of its sides by the sine of the angle between them.

Savsd = AВ * AD * Sin60 = 10 * 15 * √3 / 2 = 75 * √3 cm2.

Second way.

Let’s build the height of the HВ.

In a right-angled triangle AВН Sin60 = ВН / AВ.

ВН = AB * Sin60 = 10 * √3 / 2 = 5 * √3 cm.

Then Savs = AD * ВН = 15 * 5 * √3 = 75 * √3 cm2.

Answer: The area of the parallelogram is 75 * √3 cm2.