Find X
Find "x"
There are lot of ways to do this.
So I may even wait for a bit longer to put the answer.
It's shared. My maths teacher gave it to me.
It took me 3 days to solve it.
Also this is my first trick I am posting so don't be very rude!
Tags: It's real Geometry!!
submitted by - abdeali kothari
/|\
/ | \
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/ |x \
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/ 30 | 46 \
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There are lot of ways to do this.
So I may even wait for a bit longer to put the answer.
It's shared. My maths teacher gave it to me.
It took me 3 days to solve it.
Also this is my first trick I am posting so don't be very rude!
Tags: It's real Geometry!!
submitted by - abdeali kothari
Labels: SharedPuzzle
posted by Rajesh Lal at
9:20 AM
49 Comments:
/|\
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/ |x \ <-- Here it is!!!!
/ | \
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/ 30 | 46 \
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woohoo.. first post..
oops.. my tree collapsed.. haha
I can solve this question .............but i want you to specify the point that the middle line is an angle bisector in your question..............DEN I CN GIVE YOU THE ANSWER !!!!!!!!!!!!!!!!!!!!!!!
Assuming that the line going from the top to the base forms a 90 degree angle with the base, there is no way it can be an angle bisector. The angles of the left triangle would be 30-60-90 and the right one would be 46-44-90. Obviously, 44 and 60 are not equal so that line is not an angle bisector. What I need to know is whether the angles formed by the base and x really are 90 degrees. I think it's a pretty safe assumption, but you still need to put information like that in the question.
is it isoceles? cause if not there theres no answer unless you want the answer in terms of other variables like the different angles it can have
im glad im a sophmore and just got done with our triangle chapter but im still confused, so the middle line isn't an angle bisector by the definition of an angle bisector,
the angles in the first triangle (counterclockwise) starting from the known are 30, 134, and 16,but idk anything else because the 2 triangles arent congruent. Hope thats help someone figure it out
there are two possible cases with that diagram
case 1: The two given angles are at the corners of the big triangle; in this case x is between 0° and 104° exclusive
(0° < x < 104°)
case 2: The 46° is between the middle line and the base; in this case x is between 0° and 136° exclusive
(0° < x < 136°)
in conclusion, not enough information is given for this question to be solved, or Euclid's Brother is correct
Oh, also i cant remember the type but i was discussing with my teacher and she said there was a type of ether geometrey or algebra in which a right angle isn't always 90 degrees.That could be the path to go
Without a length it is impossible to solve for the lenght of X, but it is possible to give the length as a proportion of something else.
X = 0.3707 of whatever the base is.
hjg
Are we sure 30 and 46 are angles?
I saw them first as lengths, which makes this a tough bit of a Trigonometry which I have no idea if it works out. But if it did it would be:
30 Sq + x Sq = Left Diagonal Sq
46 Sq + x Sq = Right Diagonal Sq
Am I way off here?
Hey guys im really surprised that i received soo many answers to my question!
S0 please note the following,
1) Windymiller, they are angles.
2) The line is not a angle bisector, itz a median.
3) Euclid's Bro That's NOT funny.4)STOP ASSUMING THAT THE LINE GOING FROM THE TOP TO THE BASE IS 90degrees!!
5)It is not an isoceles
LAST: Ill write and check answers 2morro again so if u have any questions...POST THEM!
Also unless I am mistaken there was a similar problem in the CAT exam.(NOONE GOT IT RIGHT).
So if i dont get any answer close to the real answer by 2morro or ay after, ill give ull a GOOD hint.
When you post problems, make sure the problem is clear. You haven't said anything about what those numbers are, and that makes it confusing. It's okay that a problem is tough, but make sure people know what problem they're trying to solve. Good first post.
x=16 degrees...
assuming, 30 is degrees of leftmost angle, 46 is degrees of center line to base angle, and you're looking of the angle X.
Steve u r completely off track and ty for the advice ill keep it in mind for my next question i ask(if there is one).Also i couldnt dram the image properly with the limited symbols on the keyboard XD.
My answer is correct given that the question, as worded, lets me arrive at that answer. That is the answer to the question as I interpret it. If that's not the question, then please clarify what the question is:
Is x an angle or length? (Or a volume? Or a typo?)
What is 46 a measure of?
That you can't draw properly with a limited character set is not really the point, since you still need to let us know what the question is.
If x is a length, are you looking for the side ratios?
And, yes, Euclid's answer was funny :)
I first assumed x as a length,
and given an answer above.
But if x is an angle, then it's value is 44 degrees
hjg
alberto ayala says:
EASY, as sin 30= x/left hypotenuse, then x= (sin 30°)*(left hypotenuse),
or x= (sin 46°)*(right hypotenuse), whatever triangle sides measuremenet
:)
So I think what we have is:
A triangle with lower left angle of 30 degrees, lower right of 46 degrees. The question is what is the angle between the right side and the median drawn from the top vertex to the bottom side.
The top angle of the triangle is 104 (180 - 30 - 46). So the angle on the left side of the median is 104-x. If we call length of half of the bottom side A, and the length of the median L, for the left half by Law of Sines, we get:
A/L = sin(104-x)/sin(30)
and for the right half:
A/L = sin(x)/sin(46),
since sin(30) = 1/2,
sin(x)/sin(46) = 2sin(104-x)
From trig identities,
sin(104-x) = sin(104)cos(x)-cos(104)sin(x)
So, sin(x)/sin(46) = 2sin(104)cos(x) - 2cos(104)sin(x)
sin(x)[1/sin(46) + 2cos(104)] = cos(x)[2sin(104)]
tan(x) = [2sin(104)] / [1/sin(46) + 2cos(104)]
x = 64.96588 degrees
Ans. To Steve:
1)all values and variables are angles.
2)the angles known are the following(anticlockwise):30(lower left), 16(part of the above), x(second part of the above angle), y(just a term im usin it is an unknown angle), 46(left of median), 134(right of median).
Anonymous after Steve how do u get 44?????!
Next Anonymous: That is not correct as trignometry is for sides, x is an angle.
Surge ill take sometime to figure out what u have written so ill tell u later, but till now ALL the answers are wrong!?
HINT: Ill give the hint i promised in about 3 hours from now.
One more thing i needed to say Surge yor solution is wrong because 46 is for right of "median" NOT the right angle of the whole triangle (the diagram came better in the email.) The 46 is supposed to be near the median it came in the middle. Sorry i didnt see that b4.
this is a better diagram(i think so)
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/ 30 degrees |46 degrees \
-----------------------------------
this is a better diagram(i think so)
/|\
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/ 30 degrees |46 degrees \
-----------------------------------
ook now i saw that it didnt come as well as i did it sorry.
Thw website doesnt put the spaces.
But the main idea is that the base angles are as follows(left - right) 30, 134, 46, unknown angle.
All the answers were wrong because people thought that the angles were: 30, unknown, unknown, 46.
So im really sorry for the diagram.
How I got 44 degrees?
Simple, If the line down the middle is a meridan, then it forms a right angle with the base, so the angle, x must be 90-46 = 44.
hjg (my anonymous handle)
To: Abdeali Kothari
Above you said one angle was 16 degrees... that's incorrect, the other half of the top angle is 60 degrees.
The left triangle is a 30-60 right triangle, and the right one is a 46-44 right triangle.
hjg
Now you say the middle line meets the middle of the base?
(No wonder no one got it right.)
If so then x = 50 degrees
hjg
Sorry, correction...
X = 64.966 degrees if it meets the middle of the base. and the other part of the top angle is 39.034 degrees.
hjg
ok, now I see what you mean, if the other half of the angle is 16 degrees, the triangle must look like this... I hope my "tree" does not fall... /\
/ / \
/ / x \
/ / \
/ / \
/ / \
/ / \
/ / \
/ / \
/ / \
/ / \
/_30________/46__________________ \
where x = 32.7272
hjg
...
....................../\............
...................././x\...........
................../../...\..........
................/.../.....\.........
............../..../\......\........
............/...../\........\.......
........../....../\..........\......
......../......./\............\.....
....../......../\..............\....
..../........./\................\...
../........../\..................\..
/_30________/46___________________\.
where x=32.7272
hjg
The angle was easier to solve than drawing this pic.
....................................
....................../\............
...................././x\...........
................../../...\..........
................/.../.....\.........
............../..../.......\........
............/...../.........\.......
........../....../...........\......
......../......./.............\.....
....../......../...............\....
..../........./.................\...
../........../...................\..
/_30________/46___________________\.
....................................
where x=32.7272
hjg
HMmm...
hjg your answer is near correct but tell me how u got it because it isnt exactly correct just near. (I am not posting the hint now)
HMmm...
hjg your answer is near correct but tell me how u got it because it isnt exactly correct just near. (I am not posting the hint now)
more decimals?
How about
32.37950696
hjg
Thanks for explaining the problem better. I get 32.72716352 degrees as well.
I calculated the relative sizes of the unit (hyp=1) triangle bases, used that to calculate missing angle, then finally subtracted known top angles from 60 degrees total to get missing x.
30:60:90 base for unit triangle is .5/tan(30)=.87
46:?:? base for unit triangle is .5/tan(46)=.48
The base of the missing, undrawn part of the 30:60:90 unit triangle is .87-(2*(.87-.48))=.10
The base angle of the missing, undrawn unit triangle is atan(.5/.10)=79 degrees
Top angle of the undrawn triangle is 11 degrees.
total top angle (30:60:90 triangle) is 60 degrees and we know two of them, so
x=60-16-11 = 32.72716352 (with math done at full precision.
Diagram: http://htatlanta.com/answer.gif
Steve is right,
I rechecked and got 32.72716352 degrees
hjg
Simplified solution (all in degrees):
a=30; b=46
x=atan( 0.5/(cot(b)-cot(a)/2) )-b
Not useful for much, but it's interesting how such a complicated solution reduces to something manageable.
Find X
Create a 30-60 right triangle adding j and height
find e then d
use law of sines to find hyp
find height and j, k
then x = 60 - d - k
a.=.....30
b.=.....46
base.=..100
e.=.....134.............=180-b
d.=.....16..............=180-a-e......Note:SINd.is.the.sine.function.in.degrees
hyp=....260.9732626.....=SINd(e)*base/SINd(d)..........(law.of.sines)
height.=130.4866313.....=SINd(a)*hyp
j.=.....26.00947509.....=SQRT(hyp^2-height^2)-2*base
k=......11.27283648.....=ATANd(j/height)
x.=.....32.72716352.....=60-d-k
hjg
well im not very good at trignometry but the answer on the whole is WRONG.
u see as i told b4 i tried for 3-4 days to solve it. Finally i thought that it was a waste of time to think abut this puzzle all the time. So to find the answer i just DREW the diagram with the angles and the answer i got for x was 30. Try it urself. So the theory and practical have to match... rite??
Now with the little trignometry i know i found another solution that gives u around 30 degrees(because surds are involved, it is approxamate.)
first i construct a line from the top vertex to the base(perpendicular line).
Then i take tan 30 and tan 46. v can find the length of the constructed height, half of the base and the constructed base.
now ext. base right most angle=46+x (ext. angle=sum of opposite int. angles).
now tan 46+x = 1/2-sq. root 3
so the angle can be found by hit and trial method on a scirntific calculator(the surd comes here so the final answer is also aproximate)
so through hit and trial i got 46+x=15
So, x=29.
Which is nearer to 30 than 32.72716352 and is much easier than all tht mumbojumbo. (In reality this was choice in this question, It was from CAT exam.)
Plz correct if i am wrong. I dont noe trignometry very well. V just started it at school.
To: Abdeali Kothari
I've checked out Steve's solution and it is correct. If he can review my solution and verify it, then you can be positive about our answer. I wish I could send a picture, but I am sure that Steve can figure out where my variable
go on his picture.
Suggestion: Trick of mind should have way to include JPG files.
hjg
MyBlog > hgeron
x=30, is the exact answer for a=30, b=45; but that's not the problem you posted.
How do you get from "i'm not very good at trig" to "the answer [we got] is wrong"?
http://htatlanta.com/answer.xlsm
[Let macros run cuz I made a cot() function]
Last I checked, 32.7 *is* "around 30" :)
You lost me at "Then i take tan 30 and tan 46. v can find the length of the constructed height, half of the base and the constructed base."
tan30 and tan46 will tell you height ratios, but the base of that triangle will be larger than the width of the base you drew in the question, so I'm not sure where you're going after that.
Instead of trial and error, check out the cool arctan function on your calculator :)
hjg, We got the same answer using different methods (there are lots of ways to solve, as Abdeali pointed out), so I'm confident we're right.
Abdeali, I drew it also, but only to get a rough idea of what the answer should be, as a double-check.
Math is "mumbojumbo"? You can just stop using all those cool inventions that wouldn't be possible without someone doing the math, then see how unimportant it is! Maybe jet pilots should just put 29k pounds in the tank when they really need 32.7k pounds? Close enough, right? (just kidding. thanks for posting the question, was a fun one to solve) ;)
To: Abdeali Kothari
I've done a lot of problems, in fact I taught at a local college for a spell (Engineering with CAD).
For students I would have changed
the 46 degrees to 45 degrees, then
the answer would have came out to
an exact degree.
Can you figure x if 46 was changed to 45 degrees?
Thanks, it was a great submission, even if half of the time was spent
figuring out the drawing.
hjg
OMG, how do u guys know this, I was thinking of the pythagoras theorem!!! whehey! anyway wast the answer, is it 42??
you guys are making this to hard.
all it has is two base values with a line seperating the two to make two right triangles. the angles are not specified and the hypotanuses are not specified therfore x is equal to all real numbers
42FTW!
michael, ya, we started there also :) 46 is the median angle, and x is an angle.
With two overlapping triangles abc and adc:
d is the midpoint of bc
angle abc is 30 degrees
angle adc is 46 degrees
what is angle dac?
44
This one is for abdeali kothari. He requested
I show him the solution, and I did, but without
the diagram, I don't think he undestood.
Here is a link to the image
http://trickofmind.com/images/puzzles/findX.png
here
u need at least one more angle named. it would be impossible to find x if without a hypotenuse
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