Question

A ramp has an angle of elevation of 15° and has a length of 19 ft. how tall is the ramp?

Answer 1

Solution

- The ramp can be visualized as shown below:

- We can see that this setup forms a right-angled triangle. This triangle has a Hypotenuse of 19ft, and an angle of 15°. How tall the ramp is, is determined by the height of the triangle, h.

- Thus, we can apply SOHCAHTOA to solve the question as follows:

$\begin{gathered} \sin\theta=\frac{Opposite}{Hyptenuse} \\ \\ \theta=15\degree,Opposite=h,Hypotenuse=19ft \\ \\ \therefore\sin15\degree=\frac{h}{19} \\ \\ \text{ Multiply both sides by 19} \\ \\ \therefore h=19\times\sin15\degree \\ \\ h=4.9175618...\approx4.92ft \end{gathered}$

Final Answer

The height of the ramp is approximately 4.92 ft