1. **State the problem:** We have a right-angled triangle with a base of 9.1 cm and an area of 23.66 cm². We need to find the size of angle $y$, which is opposite the base. 2. **Recall the formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify known values:** - Base $b = 9.1$ cm - Area $A = 23.66$ cm² 4. **Find the height $h$ using the area formula:** $$23.66 = \frac{1}{2} \times 9.1 \times h$$ Multiply both sides by 2: $$2 \times 23.66 = 9.1 \times h$$ $$47.32 = 9.1 \times h$$ Divide both sides by 9.1: $$h = \frac{47.32}{9.1} \approx 5.2 \text{ cm}$$ 5. **Use trigonometry to find angle $y$:** Since $y$ is opposite the base, and the height is adjacent to $y$, we use the tangent function: $$\tan(y) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{b} = \frac{5.2}{9.1}$$ 6. **Calculate $y$:** $$y = \tan^{-1}\left(\frac{5.2}{9.1}\right)$$ Using a calculator: $$y \approx \tan^{-1}(0.5714) \approx 29.8^\circ$$ 7. **Round to the nearest degree:** $$y \approx 30^\circ$$ **Final answer:** The size of angle $y$ is approximately $30^\circ$.