1. **State the problem:** We need to find the length of the wire that supports the tower. The wire is the hypotenuse of a right triangle where the side adjacent to the 60° angle is 120 ft. 2. **Identify the known values:** - Angle: $60^\circ$ - Adjacent side (to 60°): 120 ft - Hypotenuse: wire length (unknown) 3. **Recall the trigonometric relationship:** For a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\cos(60^\circ) = \frac{120}{\text{wire}}$$ 5. **Use the exact value for $\cos 60^\circ$ from the table:** $$\cos 60^\circ = \frac{1}{2}$$ 6. **Set up the equation:** $$\frac{1}{2} = \frac{120}{\text{wire}}$$ 7. **Solve for wire:** Multiply both sides by wire: $$\frac{1}{2} \times \text{wire} = 120$$ Divide both sides by $\frac{1}{2}$: $$\text{wire} = \frac{120}{\frac{1}{2}}$$ Show cancellation: $$\text{wire} = 120 \times \cancel{\frac{1}{\frac{1}{2}}} = 120 \times 2$$ 8. **Calculate the final length:** $$\text{wire} = 240$$ ft **Final answer:** The wire is 240 ft long.