Final answer:
To find the angle opposite the side that is 7.1 cm, we can use the law of cosines to calculate the angle using the lengths of the triangle sides. None of the given choices (A) 37 degrees, (B) 90 degrees, (C) 115 degrees, or (D) 60 degrees are possible angles.
Step-by-step explanation:
To find the angle opposite the side that is 7.1 cm, we can use the law of cosines, which states that c^2 = a^2 + b^2 - 2ab * cos(C), where c is the side opposite the angle C. In this case, a = 5.7 cm, b = 3.7 cm, and C = 53 degrees.
Substituting the values into the formula:
7.1^2 = 5.7^2 + 3.7^2 - 2(5.7)(3.7) * cos(C)
Simplifying:
50.41 = 32.49 + 13.69 - 42.18 * cos(C)
0.22 = -42.18 * cos(C)
cos(C) = -0.0052
Using an inverse cosine function, we find that the approximate angle C is 179.99 degrees.
Since angles in a triangle must add up to 180 degrees, the angle opposite the side that is 7.1 cm cannot be 179.99 degrees. Therefore, none of the given choices (A) 37 degrees, (B) 90 degrees, (C) 115 degrees, or (D) 60 degrees are possible angles.
Learn more about Triangle Angles