Thread: My Professor Challenge!

well,..from few days me and my friend have been tested by my professor with Geometry question i didnt actully seems to reach to a satisfied answer or equation dealin this,..
ok check this out;
we know from the abc geometry Fethsagorth(not sure of spelling) about calculating the hypotenuse if u got 2 known sides of the 90 triangle..
and we know also that hypotenuse values may varies between: Z numbers like; 1234,...etc
and square roots numbers like; square root 2, square root 3, square root 5 ...etc
so can u make a general equation which resulted to get the hypotenuse tall (X) in right Z numbers(1234,...etc) not square roots numbers??
here in the pic, i hit example of right Z numbers like( 7,10,..whateva right numbers)
can u make an equation that resulted X in right Z numbers also,..not square roots?
(this is just nyumbers example,..say any number but it should be right number..)
click on pic, to enlarge,..

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well you know a²+b²=c², I call it pythagorean theorem. I don't know what "Fethsagorth" is. But from what I understand you are saying that you don't want the hypotenuse to be a square root. If you want a precise number you can estimate using your calculator, or estimate roughly. Like sqrt(5) is between sqrt(9) and sqrt(4), so sqrt(5) should be about 2.2...

So, for your example c²= 7²+10² c= sqrt(149), you can't do anything to not make it square root... The answer is accurately sqrt(149) which you can estimate to be close to sqrt(144) which is like 12.1 ...

So my final answer is you can easily estimate sqrt numbers to real numbers, but you wouldn't be accurate.

i know that i will get sqrt149. but if we change the lenghtes to other acceptable number to be rooted like; 3 and 4 then we will get the hyp,(x)= 5 cm ,but if we change the other sides also to 3 and 5 we wont get right number..( 1,2,3,...etc), if we changed the two sides to 2 and 2 it will work we will get x= 4 cm,..but 2 and 3 as ex, wont work,..but.....will work,while....wont work, and.... will work, while .....wont....
can u put an equation to me describing these magical seriese in order to describe only the lenghth of hyp,(x) as a right number( not sqrt!)
this is exactly my point of qestion ,..coz i was little bet disclear..
the equation is theoritically saying; the sumission of (ab)sq + (bc)sq must give right z number (1,2,3,4,...etc) NO FOR sqrt 3,..etc
ps: yeah i meant pythagorean, but he is known in arabic with fethagorht..

Salaam! I'm Persian, up north. :P

2 and 2 it will work we will get x= 4 cm

I take x is the hypotenuse, so if a and b are 2 and 2, then the hypotenuse is 2sqrt(2).

You see, a length is a length... we cannot change the length just because we want to. If we change the length of the hypotenuse, it isn't a right triangle anymore.

3 and 5 we wont get right number..

You mean we won't get an integer. Right? We can't get an integer because the angle is set at 90º. The side opposite of this 90º angle is the hypotenuse; therefore, the only way you can change the length of the hypotenuse is to change the angle.

If you change the angle, then you have to do trig.

I don't know how to draw it for you and show that their is only one hypotenuse for two legs with 90º in between the two.

If one leg is 3, and the other is 5, and the angle in between the two is 90º, how many different triangles can you draw?

The answer is that a person can only draw one triangle with a hypotenuse of sqrt(34).

the equation is theoritically saying; the sumission of (ab)sq + (bc)sq must give right z number

Uhh, this is not correct. The equation is ab² + ac² = bc² were bc is the hypotenuse and the angle opposite of bc is 90º. Therefore bc = sqrt(ab² + ac²). bc doesn't have to be an integer, there is nothing wrong with a length having a sqrt in it, even though in the real world we don't usually say 2sqrt(2) inches... but we rather estimate it to 3.41 .

work,..but.....will work,while....wont work, and.... will work, while .....wont....

It almost always works... well if you want to get technical and say that a hypotenuse can not be a sqrt, then 5 is the same thing as sqrt(25); therefore, you'd be saying all numbers won't work.

salam to u too
well...uhh i wish i could write
that in arabic but i want all people to understand what am saying..
i know that it will work if the hyp x = sqrt34 or any other rt..but i mean can you derive an equation getting the hypX always right z numbers, i dunnt know what do u call these numbers ,may it called; right,..true...valid numbers may be..the important thing not getting the hyp as (sqrtX), hmmm i will shoot u a close example; sure u heard of this relation (2n+1) which means that we will always get numbers like (3,5,7,9,1,13..etc)
and the relation (2n) that mean we will always get numbers like (2,4,6,8,10...etc)
see?? thats mean there is a relationa one derived in order to describe only certain values..
now can u derive an equation describing getting the hypX as true number not sqrtx??
anyway if i knew the answer from my prof, i will post it here..but it was a challenge from him derserve to be discussed ..