1. **State the problem:** We have a flagpole supported by four metal braces. Each brace makes an angle of 55° with the ground and meets the pole 6.2 m above the ground. We need to find the total length of all four metal braces. 2. **Identify the known values:** - Height where braces meet the pole: $h = 6.2$ m - Angle between each brace and the ground: $\theta = 55^\circ$ - Number of braces: 4 3. **Formula used:** The braces form the hypotenuse of a right triangle where the height is the opposite side to the angle $\theta$. Using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}$$ where $L$ is the length of one brace. 4. **Solve for $L$:** $$L = \frac{h}{\sin(\theta)}$$ 5. **Calculate $L$:** $$L = \frac{6.2}{\sin(55^\circ)}$$ Calculate $\sin(55^\circ)$: $$\sin(55^\circ) \approx 0.8192$$ So, $$L = \frac{6.2}{0.8192} \approx 7.57 \text{ m}$$ 6. **Find total length of all four braces:** $$\text{Total length} = 4 \times L = 4 \times 7.57 = 30.28 \text{ m}$$ **Final answer:** The total length of the four metal braces is approximately **30.28 m**.