Question

Find the height of the platform. Explain the trigonometric ratio that you chose to use and why you chose it. Show your work, rounding to the nearest hundredth, if necessary.

Answer 1

We are given the following information.

Length of ramp = 3.5 m

Ramp's angle of elevation = 28°

We are asked to find the height of the platform.

Let us draw a diagram to better understand the problem.

Notice that it is a right-angled triangle.

With respect to the angle 28°, the opposite side is h and the hypotenuse is 3.5 m.

So, we need to use the trigonometric ratio which involves opposite and hypotenuse sides.

`\sin\theta=(opposite)/(hypotenuse)`

Substitute the known values and solve for height (h).

`\begin{gathered} \sin(28\degree)=(h)/(3.5) \\ h=\sin(28\degree)\cdot3.5 \\ h=1.64\;m \end{gathered}`

Therefore, the height of the platform is 1.64 m