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yanni
i neeeed serious help.....
what do you need help with?
In the figure below, find the exact value of y. (Do not approximate your answer.)
find the side of the larger triange, using pyth theorem
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.
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.
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
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.
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
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.
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. \[\sqrt{11-(6-y)^2}=\sqrt{5^2-y^2}\] \[11-(6-y)^2=25-y^2\] \[11-(36-12y+y^2)=25-y^2\] \[2y^2-12y-50=0\] \[\therefore y=\sqrt{34}+3\]
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?
@yanni Did you understand anything about this problem or are you more confused than when you asked the question?
Chelsea, your answer cannot be correct. Your value of y is greater than the 6 at the base of the triangle!
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.
@agent0smith Finally a voice of reason. Thanks!
haha no prob. I forgot to make the drawing:
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|
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.