Question

In ∆KLM , l =7 inches , k=9.5 inches and < K=54°. Find all possible values of

Answer 1

ANSWER:

$L=36.6\text{\degree}$

STEP-BY-STEP EXPLANATION:

We can apply the sine theorem which says the following

$\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \\ \text{ in this case} \\ \frac{k}{\sin K}=\frac{l}{\sin L} \end{gathered}$

now, replacing and solving for L

$\begin{gathered} \frac{9.5}{\sin54}=\frac{7}{\sin L} \\ \sin L=\frac{7\cdot\sin 54}{9.5} \\ L=\arcsin (0.59611) \\ L=36.59\text{\degree}\cong36.6\text{\degree} \end{gathered}$