1. **State the problem:** We have a right-angled triangle with hypotenuse 18.7 cm, one leg 15.2 cm, and we need to find angles $x$ and $y$. 2. **Recall the Pythagorean theorem and trigonometric ratios:** In a right triangle, the hypotenuse is the longest side opposite the right angle. The other two sides are legs. Angles $x$ and $y$ are acute angles. 3. **Find the missing leg:** Use Pythagoras' theorem: $$\text{other leg} = \sqrt{18.7^2 - 15.2^2}$$ Calculate: $$18.7^2 = 349.69$$ $$15.2^2 = 231.04$$ $$\text{other leg} = \sqrt{349.69 - 231.04} = \sqrt{118.65} \approx 10.89$$ 4. **Find angle $x$:** Angle $x$ is adjacent to the 15.2 cm side and opposite the other leg (10.89 cm). Use tangent: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{10.89}{15.2} \approx 0.7164$$ $$x = \tan^{-1}(0.7164) \approx 35.7^\circ$$ 5. **Find angle $y$:** Since the triangle's angles sum to 180° and one angle is 90°, $$y = 90^\circ - x = 90 - 35.7 = 54.3^\circ$$ **Final answers:** $$x \approx 35.7^\circ$$ $$y \approx 54.3^\circ$$