It appears that you correctly knew to use cosine to set up an equation, but you made a mistake in figuring the role of the 2 foot peg. 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}-{2}={8}\usepackage{cmbright}\Huge\$ feet. This is the side adjacent to the $\displaystyle{{40}}^{\circ}\usepackage{cmbright}\Huge\$ angle. The length of the rope is the hypotenuse of this right triangle.