an escalator lifts people to the second
floor, 25 ft above the first floor. the escalator rises at a 30 angle. How far does a person travel from the bottom to the top of the esalator?
To find out how far a person travels from the bottom to the top of the escalator, we need to calculate the length of the escalator's incline. We can use trigonometry to solve this problem.
First, let's denote the distance traveled by the person as "d." According to the problem, the height of the second floor above the first floor is given as 25 ft. The angle of incline is 30 degrees.
Since we have the height and the angle, we can use the trigonometric function sine (sin) to find the length of the escalator's incline. The equation to use is:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height (25 ft) and the hypotenuse is the length of the escalator's incline (d).
Rearranging the equation, we have:
d = height / sin(angle)
Substituting the given values, we get:
d = 25 ft / sin(30°)
Using a calculator or reference table, we find that sin(30°) is approximately 0.5.
d = 25 ft / 0.5
d = 50 ft
Therefore, a person will travel a distance of 50 ft from the bottom to the top of the escalator.