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In △ ABC, ∠ C = 90 ° (1) known C = 8 √ 3, ∠ a = 60 °, find ∠ B, a, B (2) known a = 3 √ 6, ∠ a = 30 °, find ∠ B, B, C That "√" is the root
First of all, C faces angle c, a faces angle a, B faces angle B, which is basic
Then (1) ∠ B = 180 ° - 90 ° - 60 ° = 30 °, sin ∠ B = sin30 ° = 1 / 2 = B / C, so 2B = 8 √ 3, B = 4 √ 3, cos ∠ B = cos30 ° = √ 3 / 2 = A / C, so a = C * √ 3 / 2 = 12
(2) As a result, C = 2A = 6 √ 6, cos ∠ a = cos30 ° = √ 3 / 2 = B / C, B = √ 3 / 2 * C = √ 3 / 2 * 6 √ 6 = 9 √ 2
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