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I have this contest question that I don't quite get how to solve.

At 10 am, the school flagpole cast a shadow 6m long. Next to the flagpole, the 0.5m high water tap cast a shadow 0.3m long. How tall is the flagpole in metres.

I have tried using proportion:

If a 0.3m long shadow was created by an object 0.5m high, Then a 6m long shadow will be created by an object 10m high.

This is assuming that the constant of proportionality is 1 and 2 thirds.

However, I don't think this is a good way to solve this problem and nor do I think the answer is correct, is there any way to solve this in a more structured way?

The Water Tap
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  • Are you thinking about similar triangles? – saulspatz Apr 11 '21 at 00:12
  • Not exactly, I was thinking more on direct proportion and rates. – The Water Tap Apr 11 '21 at 00:15
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    Draw a picture. You'll see two similar triangles. That justifies using proportion. – saulspatz Apr 11 '21 at 00:18
  • Thanks for the suggestion! – The Water Tap Apr 11 '21 at 00:19
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    "I don't think this is a good way to solve this problem and nor do I think the answer is correct," Why on earth not?! It's a law of the universe and we can assume without question that Height:: shadow is at any time and place a constant proportion and as we have height and shdaow pair (0.5 water tap with 0.3 shadow ) we know the proportion is $0.5$ to $0.3$ or $5$ to $3$. So we know $FLAGPOLE::6 = 5::3$. Or in other words $\frac x6 = \frac 53$. It's very simple and correct to solve $x = 10$. – fleablood Apr 11 '21 at 00:55
  • Thank you for the thought, I am sometimes completely unsure on my answers and my method! – The Water Tap Apr 11 '21 at 00:58
  • Are there any other ways to solve this problem, preferably using algebra? – The Water Tap Apr 11 '21 at 08:58

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