Answered

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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.

Mr Fawcett Is Building A Ramp For Loading Motorcycles Onto Atrailer The Trailer Is 28 Feet Off The Ground To Avoid Makingit Too Difficult To Push A Motorcycle O class=

Sagot :

Solution

- 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:

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

Final Answer

The length of the ramp is 10.82 feet

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