A playground slide is 14.5 feet long with an 8.5-foot tall ladder. What is the measure of the angle that the slide makes with the ground, x, to the nearest degree?
The slide and the ladder made a right angle triangle with the ground. The angle that the slide made with the ground is labeled as [tex]x[/tex] in the diagram below. We can use the trigonometry ratio to work out the size of the angle.
8.3 is the side opposite to the angle and 14.5 is the hypotenuse. We need to use the Sin ratio
[tex]Sin(x)= \frac{opposite}{hypotenuse} [/tex] [tex]sin(x)= \frac{8.5}{14.5} [/tex] [tex]sin^{-1}( \frac{8.5}{14.5})=x [/tex] [tex]x=36[/tex]° to the nearest degree
