Question

An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30o angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?

a) 50 ft
b) 43 ft
c) 87 ft
d) 25 ft

Answer 1

a person travel 50 ft from the bottom to the top of the escalator

Explanation:

An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30 degree angle

The escalator forms a right angle triangle

opposite to 30 degree angle is 25 feet. to find the distance from the bottom to the top of the escalator we find the hypotenuse

let x be the hypotenuse

`sin(theta)=(opposite)/(hypotenuse)`

`sin(30)=(25)/(x)\\x sin(30)= 25\\x=(25)/(sin(30)) \\x=50\\`

a person travel 50 ft from the bottom to the top of the escalator