1. **Problem statement:** We need to find the height $y$ of an isosceles triangle where the two equal sides each measure 11.5 m and the angle adjacent to the height is 57°. 2. **Understanding the triangle:** The height $y$ splits the isosceles triangle into two right triangles. Each right triangle has a hypotenuse of 11.5 m and an angle of 57° adjacent to the height. 3. **Formula used:** In a right triangle, the height $y$ opposite the angle 57° can be found using the sine function: $$y = 11.5 \times \sin(57^\circ)$$ 4. **Calculate the sine value:** Using a calculator or sine table, $$\sin(57^\circ) \approx 0.8387$$ 5. **Calculate the height:** $$y = 11.5 \times 0.8387 = 9.64405$$ 6. **Round to 2 decimal places:** $$y \approx 9.64$$ meters **Final answer:** The height $y$ of the isosceles triangle is approximately **9.64 m**.