Can someone please help me with the problems below.

- wintersuntime

Can someone please help me with the problems below.

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- wintersuntime

##### 1 Attachment

- DanJS

an altitude forms a right angle , right?

- wintersuntime

yes

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## More answers

- wintersuntime

@sleepyjess

- wintersuntime

@nincompoop

- DanJS

sorry, here

- wintersuntime

thats okay

- DanJS

|dw:1449203832496:dw|

- DanJS

2 variables, gonna need 2 equations to figure it out probably

- wintersuntime

okay

- DanJS

|dw:1449203944647:dw|

- wintersuntime

why did you add the u?

- DanJS

broke up the distance y into the two shorter ones u and y-u, they still total y

- wintersuntime

okay

- DanJS

apply the pythagorean theorem
x^2 + u^2 = 12^2
and
x^2 + (y + u)^2 = 5^2

- DanJS

now we have 3 variables though, need another equation

- wintersuntime

okay

- wintersuntime

would it be x^2+y^2= 12^2 ?

- 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

x^2 + u^2 = 144
and
x^2 + y^2 + 2*y*u + u^2 = 25

- wintersuntime

okay

- 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

the first tells you it is 144
x^2 + u^2 = 144
and
y^2 + 2*y*u + 144 = 25

- DanJS

yeah need another info piece

- anonymous

exactly

- anonymous

though my previous comment needs an edit...
0 < x < 5

- DanJS

heron's formula

- wintersuntime

okay

- DanJS

the area of the large triangle is 1/2*y*x
heron's relates that to the three sides amd the altitude

- DanJS

the unknowns in that one will be , y and x

- 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

okay

- 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

that makes it not fun anymore

- 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

Anyone friendly with Pythagoreas?

- wintersuntime

isn't the equation for that a^2+b^2=c^2

- DanJS

yeah, i did not assume the bottom angle was right

- mathmale

He was the guy who obsessed over right triangles and came up with a very useful theorem. Yes, wintersumtime.

- wintersuntime

Alright

- mathmale

The length of the hypotenuse of the larger triangle is ... ???

- 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

wouldn't it be 13?

- mathmale

Why not take the easiest way out, and then go back and check Heron's Theorem?

- mathmale

Yes, the hyp has length 13.
How would u use this fact to determine the unknown height of the larger triangle?

- mathmale

Hint: Apply P's Theorem to the smaller triangle.

- mathmale

And use principles pertaining to similar triangles.

- wintersuntime

hmm how would you apply it to the smaller triangle though?

- 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

6.5?

- 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

oh okay, now I see.

- mathmale

So, it seems to me that the correct equation of ratios would be 5/13 = x/12. Agree or disagree?

- wintersuntime

Agree

- mathmale

5 and x pertain to the smaller triangle, whereas 12 and 13 pertain to the larger.

- mathmale

Solve for x.

- wintersuntime

I got 13x=60 but I don't know how to solve it after that

- mathmale

divide both sides of your equation by 13, to isolate x.

- wintersuntime

x=4.6

- 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

4.6 looks just about right. Is that equal to 60/13?

- wintersuntime

yes

- mathmale

Cool.

- 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

ok thanks

- mathmale

This is not to say that the other methods suggested will not work; ours is just simpler.

- mathmale

You're welcome!

- 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

Alright

- mathmale

I don't even remember Heron's Law. If you do, and can understand it, more power to you!

- DanJS

it relates the 3 side lengths to the area

- wintersuntime

okay

- wintersuntime

thanks

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