Given two sides of the triangle a = 11, b = 8√3 and ∠C = 30 °, opposite to the third side. Find the third party c.
| April 11, 2021 | education
We use to solve the cosine theorem for a triangle.
AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * Cos30.
AB ^ 2 = (8 * √3) ^ 2 + 11 ^ 2 – 2 * 8 * √3 * 11 * Cos30 = 192 + 121 – 2 * 8 * √3 * 11 * √3 / 2.
AB ^ 2 = 313 – 264 = 49.
AB = 7 cm.
Answer: The length of the third side is 7 cm.
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