Given a parallelogram ABCD with an angle of 30 and a height of 5 cm.Find the remaining angles

Given a parallelogram ABCD with an angle of 30 and a height of 5 cm.Find the remaining angles and sides of the parallelogram if its P = 44 cm.

1. The height of the ВK is drawn to the AD side.

2. The length of the AB side can be calculated through the sine ∠A:

ВK: AB = sine ∠A = sine 30 ° = 1/2.

AB = ВK: 1/2 = 5: 1/2 = 10 cm.

3. In a parallelogram, the opposite sides are equal. With this in mind, the perimeter (P) is calculated by the formula:

P = 2 (AB + AD) = 44 cm.

4. AD = 22 – AB = 22 – 10 = 12 cm.

5. ∠А + ∠В = 180 ° (according to the properties of the parallelogram).

∠А = 180 ° – 30 ° = 150 °.

Answer: ∠В = ∠D = 150 °, ∠А = ∠С = 30 °. AB = CD = 10 cm, BC = AD = 12 cm.