Final answer:
To calculate side lengths a and b in a triangle given another side c and two angles, we use the Law of Sines. Solving for side lengths a and b, they are approximately 8.04 and 8.38 units, matching option B.
Step-by-step explanation:
You would like to calculate the side lengths a and b of a triangle with angles measuring 64 degrees, 85 degrees, and the side c measuring 9.3 units. To find the lengths of sides a and b, we can use the Law of Sines:
\[\frac{a}{\sin(64^\circ)} = \frac{b}{\sin(85^\circ)} = \frac{9.3}{\sin(31^\circ)}\]
We first calculate the angle opposite to side c, which is 180 - 64 - 85 = 31 degrees. Using this, we can solve for sides a and b by cross-multiplying and then dividing:
For side a:
\[a = \frac{9.3 \cdot \sin(64^\circ)}{\sin(31^\circ)}\]
For side b:
\[b = \frac{9.3 \cdot \sin(85^\circ)}{\sin(31^\circ)}\]
Using a calculator, we find that:
\[a \approx 8.04\]
\[b \approx 8.38\]
Therefore, the correct lengths to two decimal places for sides a and b are approximately 8.04 and 8.38 respectively, which corresponds to option B.