How long does it take you to solve this geometric puzzle?

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roygoh

Senior Member
Hi,

Here's a simple geometric puzzle that I happen to come across some time ago. Without cheating (such as constucting the figure and measuring the angle to be solved), how long does it take for you to solve it mathematically?

Added rule: without using trigo functions like sin/cos/tan etc...

Please post your timing (hours, days, weeks, months....) and the angle, but not the solution.

Note, the two 80 deg marking refers to the two inner angles of the base of the main triangle. The question is to solve for the angle marked with a "?".

Have fun!

- Roy

ClubSNAP Idol
Staff member
Originally posted by roygoh
Hi,

Here's a simple geometric puzzle that I happen to come across some time ago. Without cheating (such as constucting the figure and measuring the angle to be solved), how long does it take for you to solve it mathematically?

Please post your timing (hours, days, weeks, months....) and the angle, but not the solution.

Note, the two 80 deg marking refers to the two inner angles of the base of the main triangle. The question is to solve for the angle marked with a "?".

Have fun!

- Roy

I can't see the number clearly; what's the value of the smaller angle found at the bottom left hand side? 30?

roygoh

Senior Member

I can't see the number clearly; what's the value of the smaller angle found at the bottom left hand side? 30?
OK, the top angle is 20, the left and right base agle of the main triangle is 80, the left inner angle is 60, and the right inner angle is 50.

What software did you use to view the picture? Maybe you scaled down the image? I can see the numbers perfectly on my screen at 100%.

ClubSNAP Idol
Staff member
Originally posted by roygoh

OK, the top angle is 20, the left and right base agle of the main triangle is 80, the left inner angle is 60, and the right inner angle is 50.

What software did you use to view the picture? Maybe you scaled down the image? I can see the numbers perfectly on my screen at 100%.
Ah...thanks for pointing that out Roy! Forgot that IE6 browser tends to auto-resize to fit the screen.

denizenx

Senior Member
7 mins to struggle with rememebring the formulas... 1 min to realise scale is usable.

roygoh

Senior Member
Originally posted by denizenx
7 mins to struggle with rememebring the formulas... 1 min to realise scale is usable.
What scale?

Bean

New Member

Calculate that out in 15 minutes...

denizenx

Senior Member
Originally posted by roygoh

What scale?
cos the angles are given, 20-80-80, 60-50 etc... so ;p construct lor...
for me I just use PS to measure... yeah about 30 deg...

roygoh

Senior Member
Originally posted by denizenx

cos the angles are given, 20-80-80, 60-50 etc... so ;p construct lor...
for me I just use PS to measure... yeah about 30 deg...
Well, like I said in my original post, that is considered cheating...hehe....try solving mathematically.

denizenx

Senior Member
Originally posted by Bean

Calculate that out in 15 minutes...
what's the crucial formula? A/sinA ? LOL

roygoh

Senior Member
Originally posted by Bean

Calculate that out in 15 minutes...
That's fast!

However, if you have simply guessed at 30 degrees, plugged the figure in and calculated the rest of the angles, you will find that the angles will agree even if you plug in a value like 50 degrees.

Care to PM me your solution?

Bean

New Member
Originally posted by denizenx

what's the crucial formula? A/sinA ? LOL
It's no longer fun if I expose the crucial formula I use in my calculations! Let more people have a guess first.... Am I right Roy? kekeke...

roygoh

Senior Member
Originally posted by Bean
It's no longer fun if I expose the crucial formula I use in my calculations! Let more people have a guess first.... Am I right Roy? kekeke...
Of course! Except that there isn't really a crucial formula except basic geometry....

roygoh

Senior Member
Guess I forgot to add that the real trick is to solve this without using trigonometric functions (sin/cos/tan etc), but simple geometry such as "sum of 3 internal agles of a trianle is 180 degrees" etc.

denizenx

Senior Member
dunno all my formulae.. someone pm the soln thx!

denizenx

Senior Member
what?
like:
x+y = 110
w+z = 160
x+w = 140
y+z = 130
???????????????????

roygoh

Senior Member
Originally posted by denizenx
what?
like:
x+y = 110
w+z = 160
x+w = 140
y+z = 130
???????????????????
Something like that. The problem you have is that you have listed 4 unknowns and only 2 effective equations. The reason I say that is: if you add eqn 1 and eqn 2, you end up with x+y+w+z = 270, and if you add eq 3 and eqn 4, you end up with the same x+y+w+z = 270.

You will need more equations to solve for all the unknowns.