Question

An escalator in a department store makes an angle of `45^circ` with the ground. How long is the escalator if it carries people a vertical distance of 24 feet?

Answer 1

`24sqrt(2) ~~ 33.94` ft

Explanation:

Let `x =`the length of the escalator

`sin45^@ = 24/x`

Solve for `x`: `x = 24/(sin45^@)`

Remember the exact answer from a trig. circle for `sin45^@ = sqrt(2)/2`

So, `x = 24/(sqrt(2)/2) = 24 * 2/sqrt(2) = 48/sqrt(2) * sqrt(2)/sqrt(2) = (48 sqrt(2))/2 = 24sqrt(2)` ft