Basic Math Puzzle: Find Dr. Gibbus' Angle

[The_Big_K]

CEans,

I found an interesting puzzle on the Internet here -

Puzzle#110 - http://www.archimedes-lab.org/page10b.html

The puzzle is as follows -

Find the "Professor Gibbus' Angle" below -



Difficulty Level: (2/5) , Basic Mathematics Knowledge.

Post your answers and the logic that you used to calculate the angle 'alpha'. All the best

-The Big K-

[RachaelP]

Well this is my first post so I hope I get this correct.

Rach

Here goes....

We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.

The angle of each of the triangles can be calculated by:

angle = tan-1 opposite/adjacent

So....

For the 2x1 triangle:

angle = tan-1 2 = 63.435

For the 3x1 triangle:

angle = tan-1 3 = 71.565

Therefore....

alpha = 180 - 63.435 - 71.565

So the Dr. Gibbus' Angle is 45 degrees.

[Ellie]

This can also be acheived in a simpler way as follows....

Leave computer chair and go to drawers

Rifle through drawers and find protractor

Go and sit back in computer chair

Put protractor on monitor and measure angle

Answer = 45 degrees

Ellie

[The_Big_K]

Originally Posted by Ellie

This can also be acheived in a simpler way as follows....

Leave computer chair and go to drawers

Rifle through drawers and find protractor

Go and sit back in computer chair

Put protractor on monitor and measure angle

Answer = 45 degrees

Ellie

No doubt you are a Crazy Engineer . But then, Logic is our best friend. It helps us in many situations.

Good approach, I must say. But I was wondering if anyone of us can actually tell us the solution for this problem.

-The Big K-

[djnachi]

Originally Posted by Ellie

This can also be acheived in a simpler way as follows....

Leave computer chair and go to drawers

Rifle through drawers and find protractor

Go and sit back in computer chair

Put protractor on monitor and measure angle

Answer = 45 degrees

Ellie

Hi Ellie,

Got to say., you got Humorously Smart Brain.
But i still wonder, is it actually the right way to find the Gibbus' Angle??

Regards,
Dj Nachi.

[djnachi]

Originally Posted by RachaelP

Well this is my first post so I hope I get this correct.



Rach

Here goes....

We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.

The angle of each of the triangles can be calculated by:

angle = tan-1 opposite/adjacent

So....

For the 2x1 triangle:

angle = tan-1 2 = 63.435

For the 3x1 triangle:

angle = tan-1 3 = 71.565

Therefore....

alpha = 180 - 63.435 - 71.565

So the Dr. Gibbus' Angle is 45 degrees.

Hi Rachael,
Hats Off ...
You made it so easy to understand. Me priety messy with mathematics but i still tried to apply few of my basics but eventually failed. So i really appreciate the fact that you so very well systematically got it.
Congrats !!!

Regards,
Dj Nachi.

[Rocker]

Originally Posted by RachaelP

Well this is my first post so I hope I get this correct.

Rach

Here goes....

We have 2 triangles the first 2x1 and the second 3x1 and the angle alpha is their intersection. Now we know that the sum of all 3 internal angles must equal 180 degrees so if we calculate the angles formed from the 2x1 and 3x1 triangles we can calculate alpha.

The angle of each of the triangles can be calculated by:

angle = tan-1 opposite/adjacent

So....

For the 2x1 triangle:

angle = tan-1 2 = 63.435

For the 3x1 triangle:

angle = tan-1 3 = 71.565

Therefore....

alpha = 180 - 63.435 - 71.565

So the Dr. Gibbus' Angle is 45 degrees.

I agree with the solution. But I guess there is a simpler way of calculating it. I can't calculate tan -1 mentally

[The_Big_K]

Okay, we have had lot of fun solving the problem. Its high time that we post the solution.

Have a look at this -



That was simple, what say?

-The Big K-