aw of Sines Score: \( 0 / 1 \) Penalty: 0.5 off Question In \( \Delta \mathrm{KLM}, l=210 \) inches, \( m \angle \mathrm{~K}=116^{\circ} \) and \( m \angle \mathrm{~L}=11^{\circ} \). Find the length of \( m \), to the nearest inch.

To find the length of side \( m \) in triangle \( \Delta KLM \), we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides. Here’s how you can solve it: First, calculate angle \( M \): \[ m \angle M = 180^\circ - m \angle K - m \angle L = 180^\circ - 116^\circ - 11^\circ = 53^\circ \] Now we apply the Law of Sines: \[ \frac{l}{\sin(K)} = \frac{m}{\sin(M)} \] Substituting the known values: \[ \frac{210}{\sin(116^\circ)} = \frac{m}{\sin(53^\circ)} \] First, calculate \( \sin(116^\circ) \) and \( \sin(53^\circ) \): \[ \sin(116^\circ) \approx 0.9063, \quad \sin(53^\circ) \approx 0.7986 \] Plug these into the equation: \[ \frac{210}{0.9063} = \frac{m}{0.7986} \] Calculate \( m \): \[ \frac{210 \times 0.7986}{0.9063} \approx \frac{167.160}{0.9063} \approx 184.5 \] Round to the nearest inch: \[ m \approx 185 \text{ inches} \] So the length of \( m \) is approximately 185 inches.