Question

The tailgate of a moving truck is $2\text{feet}$ above the ground. The incline of the ramp used for loading truck is $15°$ as shown. Find the length of the ramp to the nearest tenth of the foot.

Short answer

The length of the ramp is $7.7\text{foot}$.

Step-by-step solution

Step 1. Write down the given information.

The tailgate of the moving truck is 2 feet above the ground as shown in figure. And the inclination of ramp used for loading the truck is $15°$.

Step 2. Calculation.

From the given, figure it can be interpreted that in triangle ABC $AB=2\text{ft and}C=15°$. Therefore, by trigonometric ratios,

$\begin{array}{c}\sin \left(C\right)=\frac{AB}{AC}\\ \sin \left(15°\right)=\frac{2}{AC}\\ AC=2\csc \left(15°\right)\\ AC=7.7\text{foot}\end{array}$

Step 3. Conclusion.

The length of the ramp is$7.7\text{foot}$.