Find the side AC of triangle ABC where AB = 4, cosB = 1 \ 3, sinC = 2 \ 3
| April 11, 2021 | education
Since the side and 2 angles are known, it is possible to determine the second side by the theorem of sines:
AC / sin B = AB / sin C; whence AC = AB * sin C / sin B = 4 * (2/3) / 2 * √2 / 3 = 4 / √2 = 2 * √2.
Pre-calculated sin B = √ (1 – cos ^ 2 B) = √ (1 – 1/3 ^ 2) = √ (1 – 1/9) = √ (8/9) = √8 / 3 = 2 * √ 2/3.
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