1. **State the problem:** We have a right triangle with hypotenuse 13, an angle of 35°, and sides labeled $x$ (horizontal) and $y$ (vertical). We need to find $x$ and $y$ rounded to 2 decimal places. 2. **Formula and rules:** In a right triangle, the side opposite an angle is related to the hypotenuse by sine, and the side adjacent is related by cosine: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ Here, $\theta = 35^\circ$, opposite side is $y$, adjacent side is $x$, and hypotenuse is 13. 3. **Calculate $y$:** $$y = 13 \times \sin(35^\circ)$$ Calculate $\sin(35^\circ)$: $$\sin(35^\circ) \approx 0.574$$ So, $$y = 13 \times 0.574 = 7.462$$ Rounded to 2 decimal places: $$y \approx 7.46$$ 4. **Calculate $x$:** $$x = 13 \times \cos(35^\circ)$$ Calculate $\cos(35^\circ)$: $$\cos(35^\circ) \approx 0.819$$ So, $$x = 13 \times 0.819 = 10.647$$ Rounded to 2 decimal places: $$x \approx 10.65$$ 5. **Final answers:** $$x = 10.65, \quad y = 7.46$$