finding x and y angles

[liesl]

First let me say I know if you add all three angles of a triangle the answer will be 180. I am given the following information:
One angle is 3x-15
Second angle is 68
Third angle is y^2
My equation should be 3x-15+68+y^2=180
I need to solve for both x and y.
I am stumped. If someone could give me a slight nudge in the right direction I believe I can figure this out.

 

[arthur ohlsten]

3x-15+68+y^2=180
3x+53+y^2=180
3x=-y^2 + 127
x= -1/3 y^2 + 127/3 this is a parabola , open left , vertex at 127/3,0
and when x=0 y=+/- sqrt 127

plot the parabola
Answers are all the points along the curve in the first quadrant because both x and y must be positive
x= l -1/3 y^2+ 127/3] 0< y< sqrt 127 0<x<127/3

Arthur

 

[mmm4444bot]

Infinite possibilities ...

Hello:

Arthur's work shows that there is a set of infinite solutions.

Interestingly, there are only eight solutions involving whole numbers.

It turns out that y will be any whole number between 0 and 12 that is not divisible by 3. One can see this by looking at the relationship between x and y in Arthur's result for x expressed in terms of y. X must be positive, so if you think about how many thirds that can be subtracted from 127/3 without becoming negative, then you see that y has a cap that is clearly less than 12 (12^2=144).

Cheers,

~ Mark

My edits: removed ambiguous language; expanded comment regarding hypothetical restriction on set Y; fixed grammer; gave up on tex mess

 

[arthur ohlsten]

I am sorry I didn't think that integer values were what was wanted.
I misunderstood the problem.
Please only choose positive integers that lie along the parabolla in the first quadrant.
Arthur

 

[stapel]

I am sorry I didn't think that integer values were what was wanted....

It does not appear that the instructions stated this restriction. But if the poster is to arrive at a finite list of values, the assumption seems reasonable. Of course, we are then assuming that the student is indeed to provide only this finite list, and not the generalized solution you'd shown. :wink:

Either way, we're guessing. :shock:

Eliz.