Final answer:
To solve the triangle with angles A = 26 degrees and B = 51 degrees and side c = 28, angle C is found to be 103 degrees. Then, using the Law of Sines, side a is approximately 12.6 and side b is approximately 22.3, rounding to the nearest tenth. The correct answer is C. C = 103 degrees, a = 22.3, b = 12.6.
Step-by-step explanation:
To solve the triangle with the given information A = 26 degrees, B = 51 degrees, and c = 28, we can first determine the measure of angle C using the fact that the sum of angles in a triangle is always 180 degrees. So, C = 180 - A - B. Once we find angle C, we can use the Law of Sines to find the lengths of sides a and b.
Step 1: Determine angle C.
C = 180 - A - B
C = 180 - 26 - 51
C = 103 degrees
Step 2: Use the Law of Sines to find side a.
a/sin(A) = c/sin(C)
a = c * sin(A) / sin(C)
a = 28 * sin(26 degrees) / sin(103 degrees)
Step 3: Calculate the value of a and round to the nearest tenth.
a ≈ 12.6
Step 4: Use the Law of Sines again to find side b.
b/sin(B) = c/sin(C)
b = c * sin(B) / sin(C)
b = 28 * sin(51 degrees) / sin(103 degrees)
Step 5: Calculate the value of b and round to the nearest tenth.
b ≈ 22.3
Therefore, the correct answer is C. C = 103 degrees, a = 22.3, b = 12.6.