Answer:
23
Explanation:
Using the Law of Sines [Solving for Angle Measures → sin <A\a = sin <B\b = sin <C\c; Solving for Sides → a\sin <A = b\sin <B = c\sin <C], set up your proportion solving for side c with its angle measure along with another angle measure that has all the information. In this case, you would set up <C and Side c along with <B and Side b because <B and Side b are already defined. To find m<C, you have to use the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°], which is 105°. Here is your proportion:
c\[√2 + √6\4] = 24
The reason being is because you are dividing 12 by ½, which is 24, sin 105° is √2 + √6\4, and sin 30° is ½. So, you simply multiply √2 + √6\4 by 24 to get 6√2 + 6√6, which rounded to the nearest whole, is 23.
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