## Another geometry puzzle

ceptimus
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Location: UK

### Another geometry puzzle

Find the angle ϴ

triangle.png
ceptimus
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Location: UK

### Re: Another geometry puzzle

Abdul Alhazred wrote: Mon Sep 28, 2020 9:47 pm Aren't the big one and the little one similar triangles?

I'll go with that == 20 degrees.
Spoiler:
Witness
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### Re: Another geometry puzzle

30°.
Witness
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### Re: Another geometry puzzle

Abdul Alhazred wrote: Wed Sep 30, 2020 12:41 pm How did you get there?
https://en.wikipedia.org/wiki/Law_of_sines
ceptimus
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Location: UK

### Re: Another geometry puzzle

Here's the way I did it, just using basic geometry.
Spoiler:
Bruce
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Location: Massachusetts

### Re: Another geometry puzzle

Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?

Bonus questions! How long will it take for Bruce and Mrs. Bruce to argue over the best means solve this puzzle? How long will the argument last before Brucetta says, "Forget about it! I'll just eat the whole 1/3! "
Witness
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### Re: Another geometry puzzle

Bruce wrote: Sun Nov 22, 2020 5:50 pm Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?
1/12. You're joking, right? :notsure:
Bruce wrote: Sun Nov 22, 2020 5:50 pm Bonus questions! How long will it take for Bruce and Mrs. Bruce to argue over the best means solve this puzzle? How long will the argument last before Brucetta says, "Forget about it! I'll just eat the whole 1/3! "
Till late into the night, especially after lights out.

Brucetta will behave for 30 seconds (standard case) to 1 minute (on a good day).

Did I win? :mrgreen:
Bruce
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### Re: Another geometry puzzle

:figamagee:
gnome
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### Re: Another geometry puzzle

Witness wrote: Sun Nov 22, 2020 7:29 pm
Bruce wrote: Sun Nov 22, 2020 5:50 pm Brucetta requested 1/4 slice of pizza. Bruce gives her 1/3 slice of pizza. Brucetta says that's too much. What fraction of pizza will Bruce have to remove from the 1/3 slice of pizza to leave her with 1/4?
1/12. You're joking, right? :notsure:
Trick question. Regardless of the amount chosen, it will either be too much removed or too little removed.

In fact, it can be mathematically proven in R2 that the odds of slicing it at exactly the correct mark is literally zero.
Witness
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### Re: Another geometry puzzle

↑ You mean like the probability of choosing any real number?
Bruce
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### Re: Another geometry puzzle

:mrgreen: Perfect excuse to keep the whole pizza to myself.
Rob Lister
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### Re: Another geometry puzzle

Zeno might submit that there is no way to provide 1/4th a slice.
ceptimus
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Location: UK

### Re: Another geometry puzzle

What's the volume of a circular pizza with radius z, and height a?
gnome
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Location: New Port Richey, FL

### Re: Another geometry puzzle

V=πz2a
ceptimus
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Location: UK

### Re: Another geometry puzzle

Yes, or in plain ASCII, V = Pi z z a
Rob Lister
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### Re: Another geometry puzzle

What is the most cost effective size of a pizza hut pizza.
gnome
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Location: New Port Richey, FL

### Re: Another geometry puzzle

Without looking, almost always the largest size.
ceptimus
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Location: UK

### Re: Another geometry puzzle

I would say the zero-size pizza hut pizza (i.e. don't buy one from there) is the most cost-effective solution. Instead, buy one from a supermarket and warm it up yourself.
Doctor X
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