Final answer:
To solve the triangle, we can use the Law of Sines. Given the angles A and B and the side c, we can find the missing angle and solve for the lengths of sides a and b. The correct answer is choice D: (m∠ A = 41°, b = 13, c = 25.9).
Step-by-step explanation:
To solve the triangle, we can use the Law of Sines. Given that angle A is 115°, angle B is 24°, and side c is 21 units long, we can start by finding the third angle, angle C.
Since the sum of the angles in a triangle is 180°, we can find angle C by subtracting angles A and B from 180°: angle C = 180° - 115° - 24° = 41°.
Next, we can use the Law of Sines to find the lengths of sides a and b. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite to that side is the same for all three sides. In this case, we can set up the following ratios:
a / sin(A) = c / sin(C) and b / sin(B) = c / sin(C)
Plugging in the known values, we can solve for a and b:
a / sin(115°) = 21 / sin(41°) and b / sin(24°) = 21 / sin(41°)
Solving these equations will give us the lengths of sides a and b, rounded to the nearest tenth. After solving, we find that a is approximately 13 units and b is approximately 25.9 units.
Therefore, the correct answer is choice D: (m∠ A = 41°, b = 13, c = 25.9).