wintersuntime
  • wintersuntime
Can someone please help me with the problems below.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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wintersuntime
  • wintersuntime
DanJS
  • DanJS
an altitude forms a right angle , right?
wintersuntime
  • wintersuntime
yes

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wintersuntime
  • wintersuntime
@sleepyjess
wintersuntime
  • wintersuntime
@nincompoop
DanJS
  • DanJS
sorry, here
wintersuntime
  • wintersuntime
thats okay
DanJS
  • DanJS
|dw:1449203832496:dw|
DanJS
  • DanJS
2 variables, gonna need 2 equations to figure it out probably
wintersuntime
  • wintersuntime
okay
DanJS
  • DanJS
|dw:1449203944647:dw|
wintersuntime
  • wintersuntime
why did you add the u?
DanJS
  • DanJS
broke up the distance y into the two shorter ones u and y-u, they still total y
wintersuntime
  • wintersuntime
okay
DanJS
  • DanJS
apply the pythagorean theorem x^2 + u^2 = 12^2 and x^2 + (y + u)^2 = 5^2
DanJS
  • DanJS
now we have 3 variables though, need another equation
wintersuntime
  • wintersuntime
okay
wintersuntime
  • wintersuntime
would it be x^2+y^2= 12^2 ?
DanJS
  • DanJS
hmm, lets try expanding out the 2 we have from the two small triangles... no y is the total length, cant use that equation
DanJS
  • DanJS
x^2 + u^2 = 144 and x^2 + y^2 + 2*y*u + u^2 = 25
wintersuntime
  • wintersuntime
okay
anonymous
  • anonymous
I think the problem is being overcomplicated... partially because of the ambiguity of the wording... The problem only really gives the length of the two sides (5 and 12)... aside from that, we are given a right angle, which appears to be an altitude. We have no other information to infer anything about the shape of the triangle... rearranging equations still leaves us with a variable y in this case... which means the lengths of the sides vary as you change the height, which makes perfect sense... however, it means the height would need to be 0 < y < 5 to have to distinct right triangles and make any sense in regards to the picture. I think the problem wants you to interpret the entire triangle as a right angle... the hilarious thing being that the only right angle they marked would be the one from the altitude... which is really confusing in light of the picture... however, the problem would then be trivial...
DanJS
  • DanJS
the first tells you it is 144 x^2 + u^2 = 144 and y^2 + 2*y*u + 144 = 25
DanJS
  • DanJS
yeah need another info piece
anonymous
  • anonymous
exactly
anonymous
  • anonymous
though my previous comment needs an edit... 0 < x < 5
DanJS
  • DanJS
heron's formula
wintersuntime
  • wintersuntime
okay
DanJS
  • DanJS
the area of the large triangle is 1/2*y*x heron's relates that to the three sides amd the altitude
DanJS
  • DanJS
the unknowns in that one will be , y and x
mathmale
  • mathmale
For an alternative approach, if anyone is interested: Find the hypotenuse of the larger triangle, whose sides are 5 and 12. The large triangle and the small triange are similar (same angles). Use an equation involving two ratios to determine the unknown height.
wintersuntime
  • wintersuntime
okay
DanJS
  • DanJS
lol so the angle at the bottom is right, i guess yeah now reading the directions again and them wanting the total huge length for the large one
DanJS
  • DanJS
that makes it not fun anymore
mathmale
  • mathmale
The "total huge length" for the large one" is the length of the hypotenuse, right? And the sides are 5 and 12. What is the length of this hypotenuse?
mathmale
  • mathmale
Anyone friendly with Pythagoreas?
wintersuntime
  • wintersuntime
isn't the equation for that a^2+b^2=c^2
DanJS
  • DanJS
yeah, i did not assume the bottom angle was right
mathmale
  • mathmale
He was the guy who obsessed over right triangles and came up with a very useful theorem. Yes, wintersumtime.
wintersuntime
  • wintersuntime
Alright
mathmale
  • mathmale
The length of the hypotenuse of the larger triangle is ... ???
DanJS
  • DanJS
i think it may work, using the herem's formula and the two pythagorean theorems, to solve for x,y, and u anyway, not sure
wintersuntime
  • wintersuntime
wouldn't it be 13?
mathmale
  • mathmale
Why not take the easiest way out, and then go back and check Heron's Theorem?
mathmale
  • mathmale
Yes, the hyp has length 13. How would u use this fact to determine the unknown height of the larger triangle?
mathmale
  • mathmale
Hint: Apply P's Theorem to the smaller triangle.
mathmale
  • mathmale
And use principles pertaining to similar triangles.
wintersuntime
  • wintersuntime
hmm how would you apply it to the smaller triangle though?
mathmale
  • mathmale
Ratios. The smaller triangle has two sides and a hypotenuse. The longer side of the smaller triangle is our unknown. What is the length of the larger side of the larger triangle?
wintersuntime
  • wintersuntime
6.5?
mathmale
  • mathmale
Comparing the hypotenuses of the two triangles, I 'd write a ratio: 5/13. Can you write a ratio that will help y ou find the unknown height and make use of this 5/13?
wintersuntime
  • wintersuntime
oh okay, now I see.
mathmale
  • mathmale
So, it seems to me that the correct equation of ratios would be 5/13 = x/12. Agree or disagree?
wintersuntime
  • wintersuntime
Agree
mathmale
  • mathmale
5 and x pertain to the smaller triangle, whereas 12 and 13 pertain to the larger.
mathmale
  • mathmale
Solve for x.
wintersuntime
  • wintersuntime
I got 13x=60 but I don't know how to solve it after that
mathmale
  • mathmale
divide both sides of your equation by 13, to isolate x.
wintersuntime
  • wintersuntime
x=4.6
mathmale
  • mathmale
Don't bother to evaluate the resulting fraction; your answer is most accurate if you leave it as the ratio of two integers.
mathmale
  • mathmale
4.6 looks just about right. Is that equal to 60/13?
wintersuntime
  • wintersuntime
yes
mathmale
  • mathmale
Cool.
mathmale
  • mathmale
You could set up another equation of ratios to check that 60/13, but I feel confident that we're on the right track.
wintersuntime
  • wintersuntime
ok thanks
mathmale
  • mathmale
This is not to say that the other methods suggested will not work; ours is just simpler.
mathmale
  • mathmale
You're welcome!
DanJS
  • DanJS
if not told that the large triangle is right, can it be solved using the diagram i drew for x,y, and u pythagorean for 2 small triangles and heron's (law of cosine)
wintersuntime
  • wintersuntime
Alright
mathmale
  • mathmale
I don't even remember Heron's Law. If you do, and can understand it, more power to you!
DanJS
  • DanJS
it relates the 3 side lengths to the area
wintersuntime
  • wintersuntime
okay
wintersuntime
  • wintersuntime
thanks

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