In the triangle ABC AB = 8cm. Point D belongs to the side BC, with AD = 18cm, BD = 14cm, DC = 12cm. Find the side AC.
| September 18, 2021 | education
In the triangle ABD, by the cosine theorem, we define the cosine of the angle ABD.
AD ^ 2 = AB ^ 2 + BD ^ 2 – 2 * AB * BD * CosABD.
196 = 64 + 324 – 2 * 8 * 18 * CosABD.
288 * CosABD = 192.
CosABD = 2/3.
The length of the segment ВС = ВD + СD = 18 + 12 = 30 cm.
In the triangle ABC, by the cosine theorem, we define the length of the side of the AC.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * CosABS.
AC ^ 2 = 64 + 900 – 240 * 2/3 = 964 – 160 = 804.
AC = 2 * √201 cm.
Answer: The length of the speaker side is 2 * √201 cm.
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