Answer
Length of escalator $\approx$ 23.1 feet
Work Step by Step
This is an classic example of 30°–60°–90° triangle in which side opposite 60° is given and length of longest side is to be calculated-
The longest side of a 30°–60°–90° triangle is twice the shortest side and the side opposite the 60° angle is $\sqrt 3$ times the shortest side.
Given that
Side opposite 60° = 20
Therefore
Shortest side = $\frac{Side opposite 60°}{\sqrt 3}$ = $\frac{20}{\sqrt 3}$
Shortest side = $\frac{20\times\sqrt 3}{ \sqrt 3\times\sqrt 3}$ = $\frac{20\sqrt 3 }{3} $
Longest Side = 2 $\times $ shortest side = 2$\times\frac{20\sqrt 3}{3}$
Longest Side = $\frac{40\sqrt 3 }{3} \approx 23.1$
Therefore length of escalator $\approx 23.1$ feet
