1. **State the problem:** We are given the ratio \( \frac{\sin 50}{u} = \frac{\sin 55}{x} \) and the value \( u = 11.8 \). We want to find \( x \). 2. **Use the formula:** From the given ratio, cross-multiply to solve for \( x \): $$ x = \frac{u \times \sin 55}{\sin 50} $$ 3. **Substitute the known values:** $$ x = \frac{11.8 \times \sin 55}{\sin 50} $$ 4. **Calculate the sine values:** \( \sin 55^\circ \approx 0.8192 \) \( \sin 50^\circ \approx 0.7660 \) 5. **Evaluate \( x \):** $$ x = \frac{11.8 \times 0.8192}{0.7660} = \frac{9.661}{0.7660} \approx 12.61 $$ 6. **Interpretation:** The value of \( x \) is approximately 12.61 units. --- **Additional answers given:** - Answer 11.8 m corresponds to \( u \). - Answer 23 and 38 likely relate to other parts of the problem involving the quadrilateral and angles. **Summary:** Using the sine ratio and given \( u = 11.8 \), we find \( x \approx 12.61 \). --- **Note on the quadrilateral:** - Vertices: A (top), B (bottom-left), E (bottom-right), F (bottom-most). - Side AF is vertical with length 15 units. - BE = 11 units. - Angles: \( \angle FBE = 75^\circ \), \( \angle BEF = 55^\circ \), \( \angle ABF = 90^\circ \). - Right triangle at B. This geometric information can be used for further calculations if needed.