Let x represent length of the slide.
We have been given that Ron is designing a new slide for the amusement park in town. The slide makes an angle of 39 with the ground. The top of the slide is to be 9 feet off the ground. We are asked to find the length of the slide.
The slide will make a right triangle with respect to ground, where length of the slide will be hypotenuse, and height of the slide will be perpendicular with ground.
We know that sine relates opposite side of right triangle with hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(39^{\circ})=\frac{9}{x}[/tex]
[tex]x=\frac{9}{\text{sin}(39^{\circ})}[/tex]
[tex]x=\frac{9}{0.62932039105}[/tex]
[tex]x=14.301141[/tex]
Upon rounding to nearest foot, we will get:
[tex]x\approx 14[/tex]
Therefore, the length of slide should be approximately 14 feet and option B is the correct choice.
