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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