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what do you need help with?

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

i attached the problem

find the side of the larger triange, using pyth theorem

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

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

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

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

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

Is this too confusing?

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

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

@agent0smith Finally a voice of reason. Thanks!

haha no prob. I forgot to make the drawing:

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

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

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

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