3 [ Constructions on a Projection Drawing ]

In a regular quadrilateral pyramid with a lateral edge of 20, the angle between the lateral edges lying in the same face is $\frac{\pi}{3}$. A line perpendicular to one of the lateral edges and passing through a point on this edge intersects the height of the pyramid. Find the length of the segment of this line that lies inside the pyramid, if the point of intersection of this line with the height divides the height in the ratio 3:7, counting from the vertex.
## Answer

17.00

## Problem