In the triangle ABC, BC = 12 cm. Point D belongs to the AC side, with AD = 7 cm, DC = 9 cm
| August 16, 2021 | education
In the triangle ABC, BC = 12 cm. Point D belongs to the AC side, with AD = 7 cm, DC = 9 cm, BD = 9 cm. Find the length of the AB side.
In the triangle ВСD, according to the cosine theorem, we determine the value of the angle ВDC.
ВС ^ 2 = ВD ^ 2 + СD ^ 2 – 2 * ВD * СD * CosВDC.
144 = 81 + 81 – 2 * 9 * 9 * CosВDC.
162 * CosВDC = 162 – 144 = 18.
СosВDC = 18/162 = 1/9.
The angle ADB and BDC are adjacent angles, the sum of which is 180, then CosADB = Cos (180 – BDC) = -CosBDC = -1 / 9.
In triangle ABD, by the cosine theorem, we define the length of the side AB.
AB ^ 2 = AD ^ 2 + BD ^ 2 – 2 * AD * BD * CosADB.
AB ^ 2 = 49 + 81 – 2 * 7 * 9 * (-1 / 9) = 130 + 14 = 144.
AB = 12 cm.
Answer: The length of the AB side is 12 cm.
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