Question

Mr. Fawcett is building a ramp for loading motorcycles onto atrailer. The trailer is 2.8 feet off the ground. To avoid makingit too difficult to push a motorcycle off the ramp, Mr. Fawcettdecides to make the angle between the ramp and the ground15°. To the nearest hundredth of a foot, find the length ofathe ramp.

Answer 1

- The illustration described can be sketched as follows:

- From the above diagram, we can observe that the ramp forms a right-angled triangle with the ground.

- The Opposite of the triangle is 2.8 feet, the angle made by the ramp with the ground is 5 degrees., whilethe length of the ramp is labeled as x.

- Thus, we can apply SOHCAHTOA to find the value of x as follows:

`\begin{gathered} \sin\theta=(Opposite)/(Hypotenuse) \\ \\ \theta=15\degree,Opposite=2.8,Hypotenuse=x \\ \text{ Thus, we have:} \\ \sin15\degree=(2.8)/(x) \\ \\ \therefore x=(2.8)/(\sin15\degree) \\ \\ x=10.8183692544...\approx10.82ft \end{gathered}`

Final Answer

The length of the ramp is 10.82 feet