Question In Delta KLM,m=6_(3)inches,mangle K=24^circ and mangle L=42^circ Find the length of I, to the nearest inch. Answer Attemptiout of 2 l=square inches

## Step 1: Finding Angle M<br />### In $\triangle KLM$, the sum of the angles is $180^{\circ}$. We are given $m\angle K = 24^{\circ}$ and $m\angle L = 42^{\circ}$. Therefore, $m\angle M = 180^{\circ} - 24^{\circ} - 42^{\circ} = 114^{\circ}$.<br /><br />## Step 2: Applying the Law of Sines<br />### We can use the Law of Sines to find the length of side $l$. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ for any triangle. In our case, we have $\frac{l}{\sin L} = \frac{m}{\sin M}$. Substituting the given values, we get $\frac{l}{\sin 42^{\circ}} = \frac{63}{\sin 114^{\circ}}$.<br /><br />## Step 3: Calculating the Length of l<br />### We can solve for $l$ by multiplying both sides of the equation by $\sin 42^{\circ}$: $l = \frac{63 \times \sin 42^{\circ}}{\sin 114^{\circ}}$. Using a calculator, we find that $l \approx \frac{63 \times 0.6691}{0.9135} \approx 46.32$. Rounding to the nearest inch, we get $l \approx 46$.