Chapter 12, Problem 65SGR

To determine

To find: An inverse trigonometric function and Angle.

Answer to Problem 65SGR

The angle of the ramp that makes with the ground is $\theta ={30}^0$

Explanation of Solution

Given information:

A bicycle ramp is $5$ feet tall and $10$ feet long.

Given

A bicycle ramp is $5$ feet tall and $10$ feet long.

We know

  $\sin \left(\theta \right)=\frac{opposite}{hypotenuse}$

From given figure

We get

  $\begin{array}{l}\sin \left(\theta \right)=\frac{opposite}{hypotenuse}\\ \Rightarrow \sin \left(\theta \right)=\frac{5}{10}\\ \Rightarrow \sin \left(\theta \right)=\frac{1}{2}\\ \Rightarrow \theta ={\sin }^{-1}\left(\frac{1}{2}\right)\end{array}$

Required inverse trigonometric function is

  $\theta ={\sin }^{-1}\left(\frac{1}{2}\right)$

On solving

We get

  $\begin{array}{l}\theta ={\sin }^{-1}\left(\frac{1}{2}\right)\\ \Rightarrow \theta ={\sin }^{-1}\left(\sin \left({30}^0\right)\right)\\ \Rightarrow \theta ={30}^0\end{array}$

Therefore,

The angle of the ramp that makes with the ground is $\theta ={30}^0$