It appears that you correctly knew to use cosine to set up an equation. You may have made a mistake in setting up the diagram first. 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.