Final answer:
Using the law of sines, the measure of side length b is 8.303 when m∠a = 60°, m∠b = 64°, and c = 8, making option 2) the correct answer.
Step-by-step explanation:
To solve the problem, we use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all sides and angles in the triangle. Given that m∠a = 60°, m∠b = 64°, and c = 8, we can set up the following ratio:
- c / sin(c∠) = b / sin(b∠)
Where c∠ is the angle opposite side c, and b∠ is the angle opposite side b. Since we are given the measures of angles a and b, we can find angle c using the fact that the sum of the interior angles of a triangle equals 180°. Thus, c∠ = 180° - 60° - 64° = 56°.
Using this information, we can then calculate:
- b = (sin(b∠) * c) / sin(c∠)
- b = (sin(64°) * 8) / sin(56°)
After performing the calculation, we find that b is approximately 8.303, which corresponds to option 2).