Find the area of a parallelogram, the greater angle of which is 150 °, and the adjacent sides are 9 and 4 cm.

1. S – area of the parallelogram ABCD. AB = 4 cm. AD – 9 cm. ВK – height. ∠В = 150 °.

2. The angle ∠АВК, formed by the height ВK and side AB, is equal to: 150 ° – 90 ° = 60 °.

3. We calculate the length of the height of the ВK through one of the trigonometric functions ∠АВК (cosine).

The cosine of this angle is equal to the quotient of dividing the height of the ВН – leg of the right-angled triangle ABK by the hypotenuse AB:

ВK / AB = cosine ∠ABK = cosine 60 ° = 1/2.

ВK = AB x 1/2 = 4 = 1/2 = 2 cm.

4. S = AD x ВK = 9 x 2 = 18 cm².

Answer: S is equal to 18 cm².