Let x represent the length of the rope. If you draw a horizontal line from the top of the peg to the pole, you will form a right triangle. The length of the vertical leg of this triangle is $\displaystyle{10}-{1}={9}\usepackage{cmbright}\Huge\$ feet. This is the side adjacent to the $\displaystyle{{35}}^{\circ}\usepackage{cmbright}\Huge\$ angle. The rope is the hypotenuse of the right triangle. So you can use cosine to set up your equation:

$\displaystyle{{\cos{{35}}}}^{\circ}=\frac{{9}}{{x}}\Rightarrow{x}\cdot{{\cos{{35}}}}^{\circ}={9}\usepackage{cmbright}\Huge\$

$\displaystyle\Rightarrow{x}=\frac{{9}}{{{{\cos{{35}}}}^{\circ}}}=\frac{{9}}{{0.819}}\ldots={10.986}\ldots\approx{11.0}\usepackage{cmbright}\Huge\$