Geometry of Triangles

jarrhead · #1 12-10-2009, 04:13 PM

I need help with my last question on my homework.

If R = 2x2 - 7, S = 4x2 - 6x + 40, and T = 18x + 3, what is the measure of R?

Anybody care to explain this?

I would think it'd be something like:

2x^2 - 7 + 4x^2 - 6x + 40 +18x + 3

6x^2 + 12x + 36 = 180
6x^2 + 12x = 144

What do I do from here?

Thunderscreech · #2 12-10-2009, 04:15 PM

What does X equal?

Remember:
SOH/CAH/TOA

Sin=Opp/Hyp.

Cos=Adj/Hyp.

Tan=Opp./Adj.

jarrhead · #3 12-10-2009, 04:16 PM

How does sohcahtoa relate to these angles? I don't have any side lengths.

Thunderscreech · #4 12-10-2009, 04:19 PM

But you have angles. Sorry, was confused.

Find what X equals, and remember you can only have 180 degrees in a triangle.

jarrhead · #5 12-10-2009, 04:20 PM

I know we have to find what x equals. Is there some form other than guess and check for:

6x^2 + 12x = 144

standupright · #6 12-10-2009, 04:21 PM

do your algebra and remember that the sum of the angles on the inside of the triangle have to equal 180.

elgecko · #7 12-10-2009, 04:23 PM

It's been years since I took trig but couldn't you factor: 6x^2 + 12x -144 = 0 then solve for x?

jarrhead · #8 12-10-2009, 04:23 PM

I remember that.

I just don't know what to do with the square.

WAIT! Hit me.

Root it, so I get

6x + √12 = 12
6x + 2√3x = 12

Right?

Still don't know where to go.

jarrhead · #9 12-10-2009, 04:24 PM

Quote:

Originally Posted by elgecko

It's been years since I took trig but couldn't you factor: 6x^2 + 12x -144 = 0 then solve for x?

6x^2 + 12x - 144 = 0

6x^2 - 144 = 12x
6x^2/12 - 12 = x

Im lost again.

standupright · #10 12-10-2009, 04:25 PM

how many angles can you solve for so far?

standupright · #11 12-10-2009, 04:26 PM

you should be able to do r and t right?

jarrhead · #12 12-10-2009, 04:29 PM

Dont know what happened, but the x2s are squares. The site took off the superscripts.

Nah, still a square

standupright · #13 12-10-2009, 04:30 PM

Quote:

Originally Posted by jarrhead

Dont know what happened, but the x2s are squares. The site took off the superscripts.

Nah, still a square

so R = 2 times the square root of 2 minus 7?

jarrhead · #14 12-10-2009, 04:31 PM

R = 2x^2 - 7

standupright · #15 12-10-2009, 04:32 PM

Quote:

Originally Posted by standupright

so R = 2 times the square root of 2 minus 7?

if that's the case, then good luck.

A-Step-Towards · #16 12-10-2009, 04:34 PM

Quote:

Originally Posted by jarrhead

I know we have to find what x equals. Is there some form other than guess and check for:

6x^2 + 12x = 144

I am not going to attempt to bewilder anyone , i am not smart with math and just barely passed math 111 with a 81%.

BUT

triangles are solved by Pythagereom theorum (i know i did not spell it right) which is a^2+b^=c^2 it seems that you are not putting 12x squared like 12x^2.

jarrhead · #17 12-10-2009, 04:38 PM

That was after combined like terms.

We are finding angles here, A-step, not sides.

We have NO side measurements.

Disraeli Gears · #18 12-10-2009, 04:41 PM

Quote:

Originally Posted by jarrhead

6x^2 + 12x - 144 = 0

6x^2 - 144 = 12x
6x^2/12 - 12 = x

Im lost again.

Factor 6x^2 + 12x - 144 = 0. You should end up with two first power binomials multiplied together (ax + b)(cx - d)=0 (one will have a plus and the other a minus because the constant in the original equation is negative), and then you can set each binomial pair equal to zero and solve them individually. Since the signs are different, one won't work in the original equations for the angles (it'll prododuce a negative angle value or something somewhere), so the other one will be what you go with.

If it doesn't factor (I think it does but I'm not sure, I've never been good at factoring trinomials), you can use the quadratic formula which is (-b +/- sqrt(b^2 - 4ac))/2a, and you'll get your 2 x values (if the equation doesn't factor they'll be radicals).

A-Step-Towards · #19 12-10-2009, 04:43 PM

^ quadratics thasts what there called, ha i took a test on all this tuesday got a 78% and dont remember it at all.

jarrhead · #20 12-10-2009, 04:43 PM

Quote:

Originally Posted by Disraeli Gears

Factor 6x^2 + 12x - 144 = 0. You should end up with two first power binomials multiplied together (ax + b)(cx - d)=0 (one will have a plus and the other a minus because the constant in the original equation is negative), and then you can set each binomial pair equal to zero and solve them individually. Since the signs are different, one should come out to a negative and thus will be invalid for your purposes (can't have a negative angle measure).

If it doesn't factor (I think it does but I'm not sure, I've never been good at factoring trinomials), you can use the quadratic formula which is (-b +/- sqrt(b^2 - 4ac))/2a, and you'll get your 2 x values (if the equation doesn't factor they'll be radicals).

We have to have 10 problems and an hour of time on study island. Four sections.

So, basically, I have 50 problems in the other three and 9 in this one. This is the last problem I need, and if I miss it, the my grade will drop to a 90 because I won't get the blue ribbon.