SOLUTION:
Step 1:
We are to find BC. Round to the nearest hundredths
a. BC is a side
b. We are given Angle B (50), Angle C (62), and side AC (12.
c. Based on the information we are given we are to use law of sines.
Step 2:
A + B + C = 180 ( sum of interior angles in a triangle)
A + 50 + 62 = 180
A + 112 = 180
A = 180 - 112
A = 68
Step 3:
We are to apply law of sines; but note that "a" is side BC and "b" is side AC
[tex]\begin{gathered} \frac{a}{\sin\text{ A}}\text{ = }\frac{b}{\sin\text{ B}} \\ \\ \frac{a}{\sin\text{ 68}}\text{ = }\frac{12}{\sin\text{ 50}} \\ \\ a\text{ x sin 50 = 12 x sin }68 \\ 0.7660a\text{ = 12 x 0.9272} \\ 0.7660a\text{ = 11.1264} \\ \text{Dividing both sides by 0.7660} \\ \frac{0.7660a}{0.7660}\text{ = }\frac{11.1264}{0.7660} \\ \\ a\text{ =14.5253} \\ a\text{ = 14.53 units (nearest hundredths)} \end{gathered}[/tex]
CONCLUSION:
The length of side BC to the nearest hundredths is 14.53 units.
