## yanni 2 years ago i neeeed serious help.....

1. Chelsea04

what do you need help with?

2. yanni

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

3. yanni

i attached the problem

4. JuanitaM

find the side of the larger triange, using pyth theorem

5. EmmaCahoon

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.

6. mathstudent55

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

7. mathstudent55

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

8. JuanitaM

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

9. 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.

10. JuanitaM

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

11. mathstudent55

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

12. JuanitaM

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

13. 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.

14. Chelsea04

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. $\sqrt{11-(6-y)^2}=\sqrt{5^2-y^2}$ $11-(6-y)^2=25-y^2$ $11-(36-12y+y^2)=25-y^2$ $2y^2-12y-50=0$ $\therefore y=\sqrt{34}+3$

15. Chelsea04

Is this too confusing?

16. Chelsea04

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

17. mathstudent55

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

18. mathstudent55

19. agent0smith

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

20. 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.

21. mathstudent55

@agent0smith Finally a voice of reason. Thanks!

22. agent0smith

haha no prob. I forgot to make the drawing:

23. 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|

24. Chelsea04

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

25. agent0smith

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

26. Chelsea04

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

27. agent0smith

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