i neeeed serious help.....

- yanni

i neeeed serious help.....

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- anonymous

what do you need help with?

- yanni

In the figure below, find the exact value of y. (Do not approximate your answer.)

##### 1 Attachment

- yanni

i attached the problem

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## More answers

- anonymous

find the side of the larger triange, using pyth theorem

- anonymous

Okay. It is a 45 45 90 triangle. So we know the hypotenuse is five. The hypotenuse in a 45 45 90 triangle is x(sqrt2). So sqrt2 is 1.41. 5/1.41 is 3.546. So x=3.546. Since it equals x.

- mathstudent55

The three triangles are similar, so the lengths of their sides are proportional.
6/5 = 5/y

- mathstudent55

You don't know it's a 45-45-90 triangle.

- anonymous

then the side that you found is the hypothenuse of 45-45-90 triangle. using that hypotheneuse is twice as large as legs, find the size of the legs

- mathstudent55

If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

- anonymous

simple - use 45-45-90 logic that
y -y - ysqrt2
5 = ysqrt2
solve for y

- mathstudent55

@JuanitaM Why do you keep mentioning a 45-45-90 trianlge when we don't have one here?

- anonymous

yes an altitude was droppened to form 90 degree at base labeled 6

- mathstudent55

The large triangle has hypotenuse of length 6 and a leg of length 5. The other leg cannot possibly measure 5, so it's not a 45-45-90 triangle. Since all triangles are similar, none of them are 45-45-90 triangles.

- anonymous

Find the 3rd side of the triangle, label this x.
\[x=\sqrt{6^2-5^2}=\sqrt{11}\]
Then find the line going straight down the triangle, label this z. You can do this two ways (you'll need both ways).
\[z=\sqrt{\sqrt{11}^2-(6-y)^2}=\sqrt{11-(6-y)^2}\]
\[z=\sqrt{5^2-y^2}\]
If you make them equal to each other, you'll be able to solve for y.
\[\sqrt{11-(6-y)^2}=\sqrt{5^2-y^2}\]
\[11-(6-y)^2=25-y^2\]
\[11-(36-12y+y^2)=25-y^2\]
\[2y^2-12y-50=0\]
\[\therefore y=\sqrt{34}+3\]

- anonymous

Is this too confusing?

- anonymous

|dw:1360214471836:dw|
Maybe that will make it more understandable :)

- mathstudent55

@Chelsea04 Can you try to calculate your answer for y as a number rounded off to the nearest tenth?

- mathstudent55

@yanni Did you understand anything about this problem or are you more confused than when you asked the question?

- agent0smith

Chelsea, your answer cannot be correct. Your value of y is greater than the 6 at the base of the triangle!

- agent0smith

Chelsea, this is your mistake:
\[11−(36−12y+y^2)=25−y^2\]\[12y−50=0 \]
mathstudent55 has the correct answer: The three triangles are similar, so the lengths of their sides are proportional.
6/5 = 5/y
You can confirm it by using cosine.

- mathstudent55

@agent0smith Finally a voice of reason. Thanks!

- agent0smith

haha no prob. I forgot to make the drawing:

- agent0smith

I'll call that angle x
|dw:1360216763172:dw|
First, look at the bigger/outer triangle
\[\cos x = \frac{ 5 }{ 6 }\]
Now, look at the inner triangle:
\[\cos x = \frac{ y }{ 5 }\]
|dw:1360216959551:dw|

- anonymous

Right, oops!!!
That seems like a much faster way!!!

- agent0smith

once you get cosx = 5/6 and cos x = y/5, then you can equate 5/6 = y/5

- anonymous

Either way is correct, just mine was more algebraic (and a little wrong!) than trignometric.

- agent0smith

Yes, your way works (other than your mistake) but will probably take longer.

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