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A spiral staircase turns 270 degrees as it rises 10 feet. The radius of the staircase is 3 feet. What is the number of feet in the length of the handrail? Express your answer as a decimal to the nearest tenth.

 Feb 3, 2019

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 of a radius of 3 ft  turned through 270°= (3/4) of a whole revolution....in other words.....(3/4) (2pi) (3)  =  (9/2)pi ft =   4.5 pi ft


The side of the rectangle will be 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



cool cool cool

 Feb 3, 2019

Deleted.....    See Cphil's answer....   cheeky

 Feb 3, 2019
edited by ElectricPavlov  Feb 3, 2019

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