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The answer will depend on the orientation of the shape. If the arc length is less than pi*radius, and the shape is like the silhouette of an ice cream cone, then the height equals the radius.

If the arc length is greater than pi*radius and the shape is with the gap on the side (like a Pacman), then the height is 2*radius.

Between these two are more complicated answers. But I do not wish to spend time on them without knowing what exactly is wanted.

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Q: How do you find height when arc length and radius is given?
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