Nerdy post of the day: can you crack this geometry problem?

[Commie Pinko Dirtbag]

Let there be an isosceles triangle ABC with base angles of measure 80 and vertex angle of 20. A ray from the base angle C divides the angle into a 60 degree angle and a 20 degree angle. It intersects AB at L. A ray from the base angle at B divides the angle inot a 30 degree angle and a 50 degree angle. It intersects AC at K. Draw KL. What is the measure of angle KLC?

(If you want spoilers, there's a convoluted solution at http://jwilson.coe.uga.edu/EMT725/BotCan/Solution/Solution.html but there's a more elegant solution that requires the drawing of fewer lines, and only inside the triangle.)



This problem was presented by a teacher of mine when I was studying for university admittance exams. I couldn't find the solution. After he told me the solution, I felt a sudden urge to bludgeon him to death.

[WritingIsMyReligion]

1. *groans*

I don't need geometry outside of school, thanks very much.

Like right now, we're looking at degree-based (??) trig. Like I give a fuck about tangents, sines, cosines, etc. So the tangent is the opposite side over the hypotenuse. So what? :grr:

:eyes:

[jpgray]

2. To my eternal shame I have yet to even solve alarcojon's puzzle

And his takes priority, right behind my schoolwork and obsessive worry about nonsense.

[Commie Pinko Dirtbag]

5. Link? -nt

[mainegreen]

3. I hate you. I have work to do, but now all I'm doing is trying to

remember my geometry.

(I don't really hate you, I just have a neurotic compulsion to solve puzzles.)

[Commie Pinko Dirtbag]

4. Mwahahahaha

My quest for undermining the productivity of Corporate America goes on quite well! :evilgrin:

[Oeditpus Rex]

6. It was this kinda stuff

that helped me change my major from drafting to journalism.

[ZombieNixon]

7. I did it in my head, so I'm pretty sure it's wrong.

(I don't have a pencil on me).

I'm going to say 30 degrees, but that's just an educated guess (emphasis on guess, I didn't even try to do all the math).

OK, back to work. :hi:

Edit: holy crap!! :wow:

[swimboy]

11. Promise to use your powers only for good?

Great herkin' somnambulists, that's impressive!

[ZombieNixon]

12. Yeah, I should start guessing more often.

:D

[swimboy]

14. Being a good guesser is not a bad gift to have.

It has gotten me pretty far! B-)

[Dangerously Amused]

18. Sure, your answer is 30 degrees...

Everybody can figure that much out. Du-uuh. :eyes:


BUT... is that in CELSIUS or FAHRENHEIT, huh Mr. Smart Guy??? Huh?? HUH???


Hah!















:P

[ZombieNixon]

19. Longitude.

:P

[Dangerously Amused]

20. Touche'!

:rofl:


You got me. :7

[JohnKleeb]

8. The answer is Scrappy Doo right?

Reminds me one more class of math to go but its my final eek.

[KitchenWitch]

9. I am getting close!

I love this stuff.

[IA_Seth]

10. Yeah, I thought I was...

I have all the angles except the ones I need. I must be forgetting how to do something.

Boy it's sure been awhile since I knew how to do this!

[IA_Seth]

13. Woo hoo!

I got it!

Now I must collapse into a coma.

On Edit: So did others..boo hoo.

[ZombieNixon]

15. I quit trying to mental math my way through it

and just guessed based on what I already knew. Just so happened, I guessed correctly. :D

[DrGonzoLives]

16. PWN3D

30 degrees

How I did it:

You can figure out <CKB and <CLB fairly easily, since they both form triangles that you know two of the other angles of. <CKB is 50, and <CLB is 40.

The intersection of the rays we will call Q, because I like that letter.

<CQB is 70 for the same reason as above, meaning that <KQL is also 70 (when one line intersects the other, opposite angles at the intersection are equal). <KQC = <LQB = 110 degrees.

Draw a perpendicular segment from KL to Q, terminating at a point X on segment KL. This leaves you a system of three equations with four unknowns:

<KQX + <LKQ = 90
<KQX + <LQX = 70
<LQX + <QLX = 90

Subject to the constraints:

<KQX, <LKQ, <LQX, <QLX all < 90
<KQX less than <LQX

From there, I used solver to come up with the solution.

[Dangerously Amused]

17. delete

ah, nevermind.