Find the smaller angle of the parallelogram if its area is 40√3 cm, and the sides are 10 cm and 8 cm.
| September 22, 2021 | education
1. Let’s designate: parallelogram ABCD. Let us drop the height BN from the vertex B.
S = AD * BN;
BN = S: AD;
BN = 40√3: 10;
BN = 4√3.
2. Consider triangle ABN.
sin of angle NAB = BN: AB;
sin of angle NAB = 4√3: 8 = √3 / 2;
angle NAB = 60 °.
Answer: The smaller parallelogram is 60 °.
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