The Law of Sines

The Law of Sines – Example 2:

\(75+42+x=180→ 117+x=180→x=180-117=63 ^\circ \)

To find sides use the law of sines: \(\frac {a}{sin\ A}=\frac {b}{sin\ B}=\frac {c}{sin\ C}\)

\(\frac {22}{sin\ 75}=\frac {b}{sin\ 42}= \frac {c}{sin\ 63}\)

Now, use proportional ratios: \(\frac {a}{b}=\frac{c}{d} → a×d=c×b\)

\(\frac {22}{sin\ 75}=\frac {b}{sin\ 42} → b=\frac {22 × sin\ 42 } {sin\ 75} =\frac{22 × 0.67}{0.96}=\frac {14.74}{0.96}=15.35\ cm\)

\(\frac {22}{sin\ 75}= \frac {c}{sin\ 63} → c=\frac {22 × sin\ 63 } {sin\ 75} =\frac{22 × 0.9}{0.96}=\frac {19.8}{0.96}=20.62\ cm\)

Exercises for the Law of Sines

Find the side of c in the ABC triangle.

1.

2.

3.

1. \(\color{blue}{73.33}\)
2. \(\color{blue}{6.51}\)
3. \(\color{blue}{20.53}\)