SOLUTION TO LAST MONTH'S QUIZ
1. 30 ft
2. 14.91 ft
3. 8.94 ft
Notes.
1. DX^{2} = 20^{2} + 20^{2} + 10^{2} (etc.)
2. The shortest WF is perpendicular to DX, and DW is perpendicular to WX.
So by similar triangles, WF/WX = WD/DX (etc.)
3. There are several straightforward methods using vectors or calculus.
But here is a simple alternative:
The shortest SF is perpendicular to WZ.
So its length is the same as that of its projection, WF', on plane ABXW.
This is least when F' is closest to W, so WF' is perpendicular to AX.
Then by similar triangles, WF'/WX = WA/AX (etc.)
