Question

Use the law of sines to solve the triangle if possible

Answer 1

The Sine rule formula is,

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

Given:

$\begin{gathered} a=13.9in \\ A=83^0 \\ b=18.3in \\ B=? \end{gathered}$

Let us solve for solve for the measure of angle B

$\frac{13.9}{sin83^0}=\frac{18.3}{sinB}$

Therefore,

$\begin{gathered} sinB=\frac{18.3\times sin83^0}{13.9}=1.30673342266 \\ \therefore B=sin^{-1}(1.30673342266)=No\text{ solution} \end{gathered}$

Hence, there are no possible solutions for this triangle (OPTION C).