RS
Joined: Feb 11, 2014
• Posts: 8624
June 13th, 2015 at 4:22:02 AM permalink
How did you come up with that equation, Ssho?
OnceDear
Joined: Jun 1, 2014
• Posts: 6728
June 13th, 2015 at 4:38:01 AM permalink
This puzzle is a good find. A quick google revealed that it bears the name "Second-Hardest Easy Geometry Problem"

Coined Here Source (Not Solution)

Hint. You need to draw more lines to arrive at a solution
Beware. The earth is NOT flat. Hit and run is not a winning strategy: Pressing into trends IS not a winning strategy: Progressives are not a winning strategy: Don't Buy It! .Don't even take it for free.
ssho88
Joined: Oct 16, 2011
• Posts: 643
June 13th, 2015 at 4:48:42 AM permalink
Quote: RS

How did you come up with that equation, Ssho?

OnceDear
Joined: Jun 1, 2014
• Posts: 6728
June 13th, 2015 at 4:58:16 AM permalink
I've now found a solution, not using Sin function at all.

solution in 6 steps It uses the properties of isosceles triangles, of which we need a few extra
Beware. The earth is NOT flat. Hit and run is not a winning strategy: Pressing into trends IS not a winning strategy: Progressives are not a winning strategy: Don't Buy It! .Don't even take it for free.
ssho88
Joined: Oct 16, 2011
• Posts: 643
June 13th, 2015 at 5:05:33 AM permalink
Quote: OnceDear

This puzzle is a good find. A quick google revealed that it bears the name "Second-Hardest Easy Geometry Problem"

Coined Here Source (Not Solution)

Hint. You need to draw more lines to arrive at a solution

Really this is the "Second-Hardest Easy Geometry Problem" ?

And now I want to challenge people out there to solve this equation :-

sin(80)/sin(40)=sin(160-x)/sin(x)
.
.
.
tan(x) = sin(20)/[2*cos(40)-cos(20)]
.
.
.
.Anyone can solve it ?
RS
Joined: Feb 11, 2014
• Posts: 8624
June 13th, 2015 at 5:30:49 AM permalink

NYSith
Joined: May 2, 2015
• Posts: 70
June 13th, 2015 at 6:56:06 AM permalink
I came up with this by drawing it out on a post it note and doing the math.

[spoiler 30]
indignant99
Joined: Feb 23, 2015
• Posts: 250
June 13th, 2015 at 8:23:56 AM permalink
Quote: NYSith

I came up with this by drawing it out on a post it note and doing the math.

Invisible math cannot be verified.
Invisible math cannot be disputed, either.
Yeah, I made a mistake once. I thought I was wrong, when I actually wasn't. -Indignant
MaxPen
Joined: Feb 4, 2015
• Posts: 3634
June 13th, 2015 at 10:35:15 AM permalink
I solved it by looking at the picture. The ? Angle looked the same as the identified 30. I took two credit cards from my wallet and used them like a bevel to determine that the angles matched. Solved in less than 30 seconds. Took me more than 10 minutes to figure out how to do the spoiler tag though.
24Bingo
Joined: Jul 4, 2012
• Posts: 1348
June 13th, 2015 at 11:03:22 AM permalink
After a while going through middle school geometry and being unable, I wound up trying to do it with vectors, and defining my unit as the length of the base, came up with the six-equation system...

a(sin 80°) + b1 = c(sin 60°)
a(cos 80°) + b2 = c(cos 60°)
d(sin 50°) + b1 = e(sin 80°)
d(cos 50°) - b2 = e(cos 80°)
c(sin 60°) - e(sin 80°) = 0
c(cos 60°) + e(cos 80°) = 1

Six equations, six unknowns. That gave me the rise and run of the line above the angle, so drawing a straight line across, taking the arctangent, and using similar triangles gave me the same answer everyone else has. I think I might have made it a little harder than it had to be, especially when I realized what the length of the bottom part of the left leg was.
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.