3. In $\triangle A B C$, if $c=8.5 \mathrm{~cm}, b=7 \mathrm{~cm}$, and $\angle A=52$. Solve the triangle. Include a sketch of the triangle.
Answer
\(\boxed{\text{Final Answer: The measures of the sides and angles of the triangle are } a = 6.93 \, cm, B = 52.78 \, degrees, \text{ and } C = 126.32 \, degrees.}\)
Step 1 ：We are given a triangle ABC with side lengths c = 8.5 cm, b = 7 cm, and angle A = 52 degrees.
Step 2 ：We can use the Law of Sines to find the other angles and the Law of Cosines to find the third side.
Step 3 ：Using the Law of Sines, we find that angle A = 0.908 radians, which is approximately 52 degrees.
Step 4 ：Using the Law of Cosines, we find that side a = 6.93 cm.
Step 5 ：Using the Law of Sines again, we find that angle B = 52.78 degrees and angle C = 126.32 degrees.
Step 6 ：\(\boxed{\text{Final Answer: The measures of the sides and angles of the triangle are } a = 6.93 \, cm, B = 52.78 \, degrees, \text{ and } C = 126.32 \, degrees.}\)
