Spiral length

Geometry Level 3

In the above picture, the length of the blue line, which is perpendicular to the ground and touches the red line at both end points, is 10 feet and the distance from the center pole to the red line is 2 feet. When looked at from directly above, the red line SEEMS as if it forms a circle.

Find the length of the red line rounded to the nearest tenth IN FEET


Note: this problem was inspired when I was at my best friend's house and I asked him what the length of his stair case was to which he promptly responded and called me a nerd XD.

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