In a mall, a shopper rides up an escalator between floors. at the top of the escalator, the shopper turns right and walks 9.09 m to a store. the magnitude of the shopper's displacement from the bottom of the escalator to the store is 16.0 m. the vertical distance between the floors is 4.89 m. at what angle is the escalator inclined above the horizontal?

Let x represent the horizontal displacement of the top of the escalator from its bottom. The geometry of the problem and the Pythagorean theorem tell you
  x² + 4.89² + 9.09² = 16.0²
  x² = 149.4598
  x ≈ 12.22 . . . meters

Then the tangent of the angle of interest is
  tan(α) = (4.89 m)/(12.22 m)
  α = arctan(4.89/12.22) ≈ 21.8°

The escalator is inclined 21.8° above the horizontal.

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