1. The problem asks to find the length of side MK (opposite side) in a right triangle where the hypotenuse is 10 meters and the angle \( \theta = 30^\circ \). 2. We use the sine function, which is defined as \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \). 3. Substitute the given values: \( \sin 30^\circ = \frac{\text{MK}}{10} \). 4. We know \( \sin 30^\circ = 0.5 \), so: $$ 0.5 = \frac{\text{MK}}{10} $$ 5. Multiply both sides by 10 to solve for MK: $$ \text{MK} = 10 \times 0.5 = 5 $$ 6. Therefore, the length of MK is 5 meters. Final answer: \( \boxed{5 \text{ meters}} \).