The person has to travel 40 feet from the bottom to the top of the escalator
Solution:
Given that escalator lifts people to the second floor of a building, 20 ft
above the first floor
The escalator rises at a 30° angle
To find: Distance person travel from the bottom to the top of the escalator
The above scenario forms a right angled triangle where the escalator follows the path of the hypotenuse.
The diagram is attached below
In the right angled triangle ABC,
AC represents Distance person travel from the bottom to the top of the escalator
AB = 20 feet
angle ACB = 30 degree
We know that,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
[tex]sin 30 = \frac{20}{AC}[/tex]
[tex]\frac{1}{2} = \frac{20}{AC}\\\\AC = 20 \times 2 = 40[/tex]
So the person has to travel 40 feet from the bottom to the top of the escalator
