In the parallelogram ABCD AB = 6, AD = 4, BD = 2√7 find AC
| August 9, 2021 | education
In triangle ABD, using the cosine theorem, we determine the cosine of the angle BAD.
BD ^ 2 = AD ^ 2 + AB ^ 2 – 2 * AD * AB * CosВAD.
28 = 16 + 36 – 2 * 4 * 6 * CosВAD.
48 * CosBAD = 52 – 28 = 24.
CosBAD = 24/48 = 1/2.
Angle BAD = 60.
Then the angle ADC = (180 – 60) = 120.
In the triangle ADC, by the cosine theorem, we define the length of the segment AC.
AC ^ 2 = AD ^ 2 + CD ^ 2 – 2 * AD * CD * Cos120 = 16 + 36 – 2 * 4 * 6 * (-1/2) = 52 + 24 = 76.
AC = 2 * √19 cm.
Answer: The length of the AC diagonal is 2 * √19 cm.
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