The number of feet in the length of the handrail is 17.3 ft.
The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle
The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft turned through 270°= (3/4) of a whole revolution
(3/4) (2pi) (3) = (9/2)pi ft = 4.5 pi ft
The side of the rectangle will be the rise of the staircase = 10ft
And the diagonal of the rectangle will be the length of the handrail
We can use the Pythagorean Theorem to solve this
Handrail length = √ [ (4.5 pi)^2 + 10^2 ] ≈ 17.3 ft
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Learn more about the Pythagorean theorem here: https://brainly.com/question/343682
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