Question

Hello! I need help please to answer this question the calculator has to be in degree mode

Answer 1

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

`\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} \\ (0.7660a)/(0.7660)\text{ = }(11.1264)/(0.7660) \\ \\ a\text{ =14.5253} \\ a\text{ = 14.53 units (nearest hundredths)} \end{gathered}`

CONCLUSION:

The length of side BC to the nearest hundredths is 14.53 units.