Question

In ∆KLM, l= 56 inches , k =27 inches and < K=10°. Find all possible values of < L, to the nearest degree.

Answer 1

In this question, we are meant to find the possible values of

This is just an application of SINE RULE, which says that:

`\begin{gathered} \frac{L}{\sin\text{ L}}\text{ = }\frac{K}{\sin \text{ K}},\text{ we have that:} \\ \\ \frac{56}{\sin\text{ L }}\text{ = }\frac{27}{\sin \text{ 10}} \\ \text{cross}-\text{ multiplying, we have that;} \\ 27\text{ x sin L = 56 X sin 10} \\ \sin L\text{ =}\frac{56\text{ X sin 10}}{27} \\ \sin \text{ L = }\frac{56\text{ X 0.1736}}{27} \\ \\ \sin \text{ L = }\frac{9.\text{ 7216}}{27} \\ \sin L\text{ =0.3600} \\ \text{Taking sine inverse of both sides, we have:} \\ L=21.1^0 \\ L=21^{0\text{ }}(\text{correct to the nearest degr}ee) \end{gathered}`