Q67. - Algebra 1

Question

How long is the ramp?

Step-by-Step Solution

Answer

The ramp is $6 \mathrm{feet}$ long.

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:

$$\begin{gathered} \sin \left(\angle A\right)=\frac{\text{leg opposite }\angle \text{A}}{\text{hypotenuse}} \\ \cos \left(\angle A\right)=\frac{\text{leg adjacent to }\angle \text{A}}{\text{hypotenuse}} \\ \tan \left(\angle A\right)=\frac{\text{leg opposite }\angle \text{A}}{\text{leg adjacent to }\angle \text{A}} \end{gathered}$$

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,

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

Therefore, the ramp is 6 feet long.