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## Quiz of the Month (December 2005)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  30 ft
2.  14.91 ft
3.  8.94 ft```

Notes.

1. DX2 = 202 + 202 + 102 (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.)

#### THIS MONTH'S QUIZ

Two vertical flag poles stand on level ground. The top of each pole is joined to the base of the other by a straight cord, and the two cords cross at a point X.

1. If the heights of the poles are 6m and 3m respectively, how high is X above the ground?

2. Alternatively, if the longer pole is 6m high and the point X is 2.5m above the ground, how high is the shorter pole?

3. With the data of Q.2, if the two poles are 12m apart, how far is X from the longer pole?

***

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