In the parallelogram ABCD, the side AB = 2, and the base AD = 1, the sine of the angle A = 1/2

univerkov | June 10, 2021 | education

In the parallelogram ABCD, the side AB = 2, and the base AD = 1, the sine of the angle A = 1/2. find the greater height of the parallelogram.

1. BE and BK – heights drawn to AD and CD, respectively. S is the area of the parallelogram.

2. Sine ∠A = 1/2. Therefore ∠А = 30 °

3. In rectangular ∆ABE, the height of BE is the leg opposite to ∠A, equal to 30 °, and the side AB of the parallelogram is the hypotenuse.

Therefore, BE = 1 / 2AB = 2: 2 = 1 unit.

4. S = AD x BE = 1 x 1 = 1 unit of measure².

5.S = CD x BK. AB = CD.

BK = 1: 2 = 0.5 units.

Answer: BE = 1 unit of measurement – great height.

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