Question In Delta LMN,l=170inches,mangle M=121^circ and mangle N=40^circ Find the length of n to the nearest inch. Answer Attemptiout of 2 n=square inches

## Step 1: Finding Angle L<br />### The sum of angles in a triangle is 180°. We have $m\angle M = 121^{\circ}$ and $m\angle N = 40^{\circ}$. Therefore, $m\angle L = 180^{\circ} - 121^{\circ} - 40^{\circ} = 19^{\circ}$.<br /><br />## Step 2: Applying the Law of Sines<br />### We can use the Law of Sines to find the length of side n. 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 $\frac{l}{\sin L} = \frac{n}{\sin N}$. Plugging in the known values, we get $\frac{170}{\sin 19^{\circ}} = \frac{n}{\sin 40^{\circ}}$.<br /><br />## Step 3: Solving for n<br />### We can solve for n by multiplying both sides of the equation by $\sin 40^{\circ}$: $n = \frac{170 \times \sin 40^{\circ}}{\sin 19^{\circ}}$. Calculating this gives $n \approx \frac{170 \times 0.6428}{0.3256} \approx 336.03$. Rounding to the nearest inch, we get $n \approx 336$.