Given a triangle with b= 3, c=9, and m∠A=118, what is the length of a? Round the answer to two decimal places. [D] 6.96 [C] 8.04 [A] 10.13 [B]10.74

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We have a triangle with side b equals 3, side c equals 9, and angle A equals 118 degrees. We need to find the length of side a using the Law of Cosines. To solve this problem, we use the Law of Cosines. The formula is a squared equals b squared plus c squared minus 2bc cosine A. Now we substitute our known values: b equals 3, c equals 9, and angle A equals 118 degrees. Let's calculate step by step. First, we have a squared equals 3 squared plus 9 squared minus 2 times 3 times 9 times cosine 118 degrees. This simplifies to 9 plus 81 minus 54 cosine 118 degrees, which equals 90 minus 54 cosine 118 degrees. Now we need to calculate cosine of 118 degrees, which is approximately negative 0.46947. Substituting this back, we get 90 minus 54 times negative 0.46947, which equals 90 plus 25.35138, giving us 115.35138. Now we take the square root of 115.35138 to find a. The square root gives us approximately 10.74017. Rounding to two decimal places, we get a equals 10.74. Therefore, the answer is choice B, 10.74.