Question

1. Jeremy is going to show off his skateboarding skills. He has a ramp that must beset up torise from the ground at a 30° angle. If the height from the ground to the platform is 8 feet,how far is the end of the ramp to the base of the platform? How long is the ramp up to thetop of the platform?

Answer 1

this is a question that involves angle of elevation and right angled triangles.

first, a diagram deoicting the scenerio is drawn below;

using the SOHCAHTOA rule for right angled triangles, we would name he distance of the ramp to the platform; x

y is length of the ramp up to the platform (the side opposite the right angle), H

8ft is the height from the ground to the platform ( the distance of the side opposite the angle), O

x is the length of the end of the ramp to the base of the platform( is the adjacent) A

THEREFORE, we will be applying TOA

`\begin{gathered} \tan \theta=\text{ opposite/adjacent} \\ \cos 30=(O)/(A) \\ \cos 30=(8)/(X) \\ 0.8660=(8)/(x) \\ x=(8)/(0.8660) \\ x=9.24ft \end{gathered}`

the end of the ramp is 9.24ft from the base of the platform

`\begin{gathered} \sin 30=\frac{posite}{\text{hypotenuse}} \\ \sin 30=(8)/(y) \\ 0.5=(8)/(y) \\ y=(8)/(0.5) \\ y=\text{ 16ft} \end{gathered}`

the ramp is 16ft long up to the top of the platform