Answer :
The value of the length of the slide is 47.1 feet.
Given-
The height of the water slide is 26 feet.
The angle between the slide and the water is 33.5 degrees.
The problem given for the trigonometry. Let height is the opposite side and the length is the adjacent side. Then by trigonometry the value of [tex]tan \theta[/tex] is equal to the ratio of opposite side [tex]b[/tex] and the adjacent side [tex]a[/tex].
Mathematically,
[tex]tan\theta =\dfrac{b}{a}[/tex]
[tex]tan33.5^o =\dfrac{26}{a}[/tex]
Rewrite the equation for the a,
[tex]a =\dfrac{26}{tan33.5^o}[/tex]
[tex]a =\dfrac{26}{0.662}[/tex]
[tex]a=39.27[/tex]
In a right angle triangle the slide being the height of the slide is opposite to the angle 33.5 degrees.
The length of the slide is [tex]x[/tex],
[tex]sin(33.5)=\dfrac{26}{x}[/tex]
[tex]x=\dfrac{26}{sin33.5}[/tex]
[tex]x=47.1[/tex]
hence, the value of the length of the slide is 47.1 feet.
For more about the trigonometry follow the link below,
https://brainly.com/question/21286835