Question

a ramp is attached to the back of a moving truck forming a 20° angle with the ground. If the ramp is 12 ft long then how high is the back of the truck off the ground?

Answer 1

Given the information on the picture, we have the following right triangle:

then, we can use the trigonometric functon sine on the angle to get the following:

`\begin{gathered} \sin (20)=\frac{\text{opposite side}}{hypotenuse}=(x)/(12) \\ \Rightarrow\sin (20)=(x)/(12) \end{gathered}`

solving for 'x', we get:

`\begin{gathered} (x)/(12)=\sin (20) \\ \Rightarrow x=12\cdot\sin (20)=4.1 \\ x=4.1 \end{gathered}`

therefore, the height is x = 4.1