The ramp forms a right triangle like this one:
Where L is the length of the ramp. As you can see L is the hypotenuse of the right triangle and the 29 ft horizontal distance is one of its legs. Here we can use the definition of the cosine of an angle in a right triangle:
[tex]\cos x=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex]Then for the 30° angle we have:
[tex]\cos 30^{\circ}=\frac{29ft}{L}[/tex]We can multiply both sides of this equation by L and divide by cos30°:
[tex]\begin{gathered} \cos 30^{\circ}\cdot\frac{L}{\cos30^{\circ}}=\frac{29ft}{L}\cdot\frac{L}{\cos30^{\circ}} \\ L=\frac{29ft}{\cos30^{\circ}} \end{gathered}[/tex]And since:
[tex]\cos 30^{\circ}=\frac{\sqrt[]{3}}{2}[/tex]We get:
[tex]L=\frac{29ft}{\cos30^{\circ}}=\frac{29ft}{\frac{\sqrt[]{3}}{2}}=\frac{2\cdot29ft}{\sqrt[]{3}}\approx33.49ft[/tex]Then the answer is 33.49ft.
