A support wire reaches from the top of a pole to a clamp on the ground. The clamp is 10 feet from the base of the pole The support wire makes a 68 angle with the ground. Find the length of the support wire

To determine the length of the support wire, we can model the situation using a right triangle: - **Adjacent side (base):** 10 feet (distance from the base of the pole to the clamp) - **Angle with the ground:** 68° - **Hypotenuse (support wire):** Unknown, which we need to find We can use the **cosine** trigonometric function, which relates the adjacent side and the hypotenuse in a right triangle: \[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \] Plugging in the known values: \[ \cos(68°) = \frac{10}{\text{Hypotenuse}} \] Solving for the hypotenuse: \[ \text{Hypotenuse} = \frac{10}{\cos(68°)} \] Calculating the cosine of 68 degrees: \[ \cos(68°) \approx 0.3746 \] Now, compute the length of the support wire: \[ \text{Hypotenuse} = \frac{10}{0.3746} \approx 26.7 \text{ feet} \] **Therefore, the support wire is approximately 26.7 feet long.**