1. **State the problem:** We need to find the total length of two slides on a playground. Each slide forms a right triangle with the ground, where the base and the angle with the ground are given. 2. **Identify the formula:** The length of each slide is the hypotenuse of a right triangle. Using the cosine of the angle, we have: $$\cos(\theta) = \frac{\text{base}}{\text{hypotenuse}}$$ which rearranges to $$\text{hypotenuse} = \frac{\text{base}}{\cos(\theta)}$$ 3. **Calculate the length of the left slide:** - Base = 64 cm - Angle = 45° $$\text{left slide length} = \frac{64}{\cos(45^\circ)} = \frac{64}{\frac{\sqrt{2}}{2}} = 64 \times \frac{2}{\sqrt{2}} = 64 \times \sqrt{2} \approx 64 \times 1.414 = 90.5 \text{ cm}$$ 4. **Calculate the length of the right slide:** - Base = 106 cm - Angle = 30° $$\text{right slide length} = \frac{106}{\cos(30^\circ)} = \frac{106}{\frac{\sqrt{3}}{2}} = 106 \times \frac{2}{\sqrt{3}} = \frac{212}{\sqrt{3}} \approx 212 \times 0.577 = 122.4 \text{ cm}$$ 5. **Find the total length:** $$\text{total length} = 90.5 + 122.4 = 212.9 \text{ cm}$$ 6. **Answer:** The total length of both slides rounded to the nearest tenth is **212.9 cm**.