Find the area of this triangle. Round the sine value to the nearest hundredth. Round the area to the nearest tenth of a centimeter.

Answer:   18.8 cm²Step-by-step explanation:Sometimes, as here, when the problem is not carefully constructed, the answer you get depends on the method you choose for solving the problem.Following directionsUsing the formula ...   Area = (1/2)ab·sin(C)we are given the values of "a" (BC=5.9 cm) and "b" (AC=7.2 cm), but we need to know the value of sin(C). The problem statement tells us to round this value to the nearest hundredth.   sin(C) = sin(118°) ≈ 0.882948 ≈ 0.88Putting these values into the formula gives ...   Area = (1/2)(5.9 cm)(7.2 cm)(0.88) = 18.6912 cm² ≈ 18.7 cm² . . . roundedYou will observe that this answer does not match any offered choice.__Rounding only at the EndThe preferred method of working these problems is to keep the full precision the calculator offers until the final answer is achieved. Then appropriate rounding is applied. Using this solution method, we get ...   Area = (1/2)(5.9 cm)(7.2 cm)(0.882948) ≈ 18.7538 cm² ≈ 18.8 cm²This answer matches the first choice.__Using the 3 Side LengthsSince the figure includes all three side lengths, we can compute a more precise value for angle C, or we can use Heron's formula for the area of the triangle. Each of these methods will give the same result.From the Law of Cosines, the angle C is ...   C = arccos((a² +b² -c²)/(2ab)) = arccos(-38.79/84.96) ≈ 117.16585°Note that this is almost 1 full degree less than the angle shown in the diagram. Then the area is ...    Area = (1/2)(5.9 cm)(7.2 cm)sin(117.16585°) ≈ 18.8970 cm² ≈ 18.9 cm²This answer may be the most accurate yet, but does not match any offered choice.