In the ABCD parallelogram, the angle a is 50 degrees, the CAD angle is 15 degrees, AC = 17.8

In the ABCD parallelogram, the angle a is 50 degrees, the CAD angle is 15 degrees, AC = 17.8, calculate the larger side of the parallelogram.

The opposite angles of the parallelogram are equal, which means <A = <C = 50 °. Sum of all angles

the parallelogram is 360 °.

<B = <D = 1/2 (360 ° – 2 * 50 °) = 130 °;

AD – large side of the parallelogram;

By the sine theorem:

AD / (sin <ACD) = AC / sin D;

<ACD = <BAC as criss-cross corners;

<BAC = 50 ° – 15 ° = 35 °;

AD = AC * sin <ACD: sin D;

sin 130 ° ≈ 0.77; sin 35 ° ≈ 0.57;

AD = 17.8 * 0.57: 0.77 ≈ 13.18.