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


Status
Not open for further replies.

roygoh

Senior Member
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#1
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

 

Adam Goi

ClubSNAP Idol
Staff member
#2
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
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#3
Originally posted by AdamGoi


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%.
 

Adam Goi

ClubSNAP Idol
Staff member
#4
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
Feb 1, 2002
4,058
0
0
41
L2TPYSG
Visit site
#9
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
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#10
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.
 

roygoh

Senior Member
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#12
Originally posted by Bean
Answer 30 degrees? :dunno:

Calculate that out in 15 minutes...:D
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
Apr 16, 2002
781
0
0
www.pbase.com
#13
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
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#14
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
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#15
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.
 

roygoh

Senior Member
Jan 18, 2002
5,011
0
0
Northwest
Visit site
#18
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.
 

Status
Not open for further replies.
Top Bottom