The sides of the parallelogram are 12 and 8 cm, and the angle between the heights drawn

The sides of the parallelogram are 12 and 8 cm, and the angle between the heights drawn from the top of the obtuse angle is 30 degrees. Find the area of the parallelogram.

1. The tops of the parallelogram – A, B, C, D. AB = 8 centimeters. AD = 12 centimeters. Heights

ВK and ВН are carried out to the sides of СD and AD, respectively. The angle between them is ∠НВК = 30 °.

S is the area of the parallelogram.

2. ∠АВН = 90 ° – ∠НВК = 90 ° – 30 ° = 60 °.

3. We calculate the length and height of the VN through one of the trigonometric functions ∠A (cosine):

BH / AB = cosine ∠ABH = cosine 60 ° = 1/2.

BH = 8 x 1/2 = 4 centimeters.

4. S = AD x BH = 12 x 4 = 48 centimeters².

Answer: S equals 48 centimeters².