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Quiz of the Month (July 2007)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ


   1.  45o,   45o,    90o
   2.  50.8o, 100.4o, 28.8o

Notes.

Q.1 Suppose the warning triangle has sides of length 2a.
It is easily seen that the dimensions of the shadow are as shown.

Q.2 Take x-y co-ordinates as shown.

Then point P can be found to be (1.2247a, 1.2247a)
So gradient of PR is 1.2247/0.2247 = 5.4504
and gradient of PQ is 1.2247/2.2247 = 0.5505

So slope of PR = tan-1(5.4504) = 79.60o
and slope of PQ = tan-1(0.5505) = 28.83o

(etc.)

THIS MONTH'S QUIZ

1. At what two times, exactly, between 12 o'clock and 2 o'clock, do the two pointers of a clock exchange positions?

2. At what two times, exactly, one time between 3 o'clock and 4 o'clock and the other between 5 o'clock and 6 o'clock, do the pointers of a clock exchange positions?

3. How many pairs of times are there between 12 noon and 12 midnight when the pointers of a clock exchange positions?

***

© Hector C. Parr (2007)

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