Question

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

Answer 1

`L=36.6\text{\degree}`

Explanation:

We can apply the sine theorem which says the following

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C) \\ \text{ in this case} \\ (k)/(\sin K)=(l)/(\sin L) \end{gathered}`

now, replacing and solving for L

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