Question

How long is the ramp?

Short answer

The ramp is$6\mathrm{feet}$ long.

Step-by-step solution

Step 1. Given. 

The triangle is given with the following dimension

Step 2. Write the formulas for the trigonometric ratios.

The formula for the trigonometric ratios is:

$$\begin{gathered} \sin \left(\angle A\right)=\frac{\text{legopposite}\angle \text{A}}{\text{hypotenuse}} \\ \cos \left(\angle A\right)=\frac{\text{legadjacentto}\angle \text{A}}{\text{hypotenuse}} \\ \tan \left(\angle A\right)=\frac{\text{legopposite}\angle \text{A}}{\text{legadjacentto}\angle \text{A}} \end{gathered}$$

Step 3. Determine the length of the ramp.

The given diagram is:

Since in the diagram, the side opposite to the angle having measure$30°$ is given and it is required to a find the hypotenuse which is the length of the ramp. Therefore, use the sine ratio.

From the diagram, it can be noticed that the leg opposite$30°$ and hypotenuse are 3, and x respectively.

Therefore,

$$\begin{gathered} \sin \left(30°\right)=\frac{\text{legopposite30}°}{\text{hypotenuse}} \\ \frac{1}{2}=\frac{3}{x} \\ 1\times x=2\times 3 \\ x=6 \end{gathered}$$

Therefore, the ramp is 6 feet long.