Answer:
17
Step-by-step explanation:
We have been given that in triangle ABC, measure of angle B is 62 degrees and measure of angle C is 48 degrees. The length of side opposite to angle a is 18.2. We are asked to find length of side b.
We will use law of sines to solve for side b.
\(\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}\)
\(m\angle A+m\angle B+m\angle C=180^{\circ}\\\\m\angle A+62^{\circ}+48^{\circ}=180^{\circ}\)
\(m\angle A+110^{\circ}=180^{\circ}\)
\(m\angle A+110^{\circ}-110^{\circ}=180^{\circ}-110^{\circ}\)
\(m\angle A=70^{\circ}\)
Upon substituting our given values, we will get:
\(\frac{18.2}{\text{sin}(70^{\circ})}=\frac{b}{\text{sin}(62^{\circ})}\)
\(\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})=\frac{b}{\text{sin}(62^{\circ})}*\text{sin}(62^{\circ})\)
\(\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})=b\)
\(b=\frac{18.2}{\text{sin}(70^{\circ})}*\text{sin}(62^{\circ})\)
\(b=\frac{18.2}{0.939692620786}*0.882947592859\)
\(b=19.1551999*0.882947592859\)
\(b=16.9130376\)
\(b\approx 17\)
Therefore, the length of side b is 17 units.