Answer: 623 inches
Step-by-step explanation:
We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise ([tex]x[/tex]) is on of the sides of the triangle (as shown in the figure).
So, if we want to find [tex]x[/tex] we have to use the trigonometric function sine:
[tex]sin(15\°)=\frac{opposite-side}{hypotenuse}[/tex] (1)
Here, the opposite side is [tex]x[/tex] and the hypotenuse is [tex]200 ft 9 in[/tex].
Now we have to transform [tex]200 ft 9 in[/tex] to inches, in this case we only have to convert [tex]200 ft[/tex] to inches, knowing that [tex]1 ft=12 in[/tex]:
[tex]200 ft \frac{12 in}{1 ft}=2400 in[/tex]
[tex]200 ft + 9 in=2400 in+ 9 in=2409 in[/tex]
Substituting this value in (1):
[tex]sin(15\°)=\frac{x}{2409 in}[/tex] (2)
Isolating [tex]x[/tex]:
[tex]x=frac{sin(15\°)}{2409 in}[/tex]
Finally:
[tex]x=623.49 in \approx 623 in[/tex]
