In an isosceles triangle ABC, the base is AC = 8 cm. Cos angle B = 1/3. Find the length of side AB.
| July 1, 2021 | education
In an isosceles triangle ABC, the base is AC = 8 cm; cos B = 1/3.
AC² = AB² + BC² – 2 * AB * BC * cos B; AB = BC;
AC² = 2 AB² – 2 * AB² * cos B;
AC² = 2 AB² (1 – cos B);
AB² = 1/2 AC²: (1 – cos B);
AB² = 1/2 * 64: (1 – 1/3); AB² = 32: 2/3; AB² = 48;
AB = √48; AB = 4 √3.
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