The sides of the parallelogram = 6 and 7 cm, the angle between them is 60 degrees. Find the heights of the parallelogram.

univerkov | July 29, 2021 | education

1. The tops of the parallelogram – A, B, C, D. AB = 6 centimeters. AD = 7 centimeters. The heights BK and BH are drawn to the sides CD and AD, respectively. ∠А = 60 °.

S is the area of the parallelogram.

2. We calculate the length of the height BH through one of the trigonometric functions ∠A (sine):

BH / AB = sine ∠A = sine 60 ° = √3 / 2.

BH = 6 x √3 / 2 = 3√3 centimeters.

2. S = АD х ВН = 7 х 3√3 = 21√3 centimeter².

3. S = AB x BK = 21√3 centimeter².

BK = 21√3: 6 = 7√3 / 2 centimeters.

Answer: BH = 3√3 centimeters. BK = 7√3 / 2 centimeters.

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