Help me find a hypotenuse.

I need to find a hypotenuse and my geometry is failing  me. I have a right triangle. A and B are equidistant so my angles are 90, 45, and 45. My perpendicular bisector to the hypotenuse is 4.5. What's my hypotenuse? 

9? I think I'm picturing what you are describing.

If I'm understanding this correctly, your hypotenuse is 9. In this picture, you're trying to find Y, right?

When you cut an isosceles right triangle in half from the right angle, you get another, smaller isosceles right triangle.

If you want more detail, as I skipped a step or two in this "proof"  here, happy to give it in the morning. 

That looks right. I found a bunch of tutorials,  but was unsure what they were labeling A B C as, the sides or the angles.

What's the application?

Use a Trig calculator.  Google it and there are tons.  Or, there are apps.  You really don't need it for this though.

http://www.carbidedepot.com/formulas-trigright.asp

I would make a smaller triangle (the blue one in the second image below) inside of your original triangle with 4.5 as one leg of the the new smaller triangle.  The angle is still 45 degrees so the other angle is 45 degrees which means the other leg (half of your original triangle is the same 4.5.  So, the hypotenuse is 9.0 of the original larger triangle.

9.0 is what I get.

mtn said:

What's the application?

4" pvc pipe through the floor. OD is 4.5" Want to figure what size wall is needed box it in.

Sin 45deg is 1.414 so your hypotenuse should be 1.414x the length of one of the other sides

Appleseed said:

mtn said:

What's the application?

4" pvc pipe through the floor. OD is 4.5" Want to figure what size wall is needed box it in.

In that case won't your hypotenuse be 4.5" + 0.5"(or whatever the thickness is of the material you're boxing it in with)?

The pipe isn't going to reach all the way into to 90* angled corner so your dimension isn't 4.5".  More math needed or just throw the pipe into a corner and see how far it sticks out.

mtn said:

If I'm understanding this correctly, your hypotenuse is 9. In this picture, you're trying to find Y, right?

 

When you cut an isosceles right triangle in half from the right angle, you get another, smaller isosceles right triangle.

 

If you want more detail, as I skipped a step or two in this "proof"  here, happy to give it in the morning. 

Your proof is flawed. In your pic, x^2 + x^2 = 81, not 9. 

I'm missing why so much math. 
 

Cut a bigger hole, make it as tight as you can, patch back. 
 

It's not more work to make a slightly bigger hole. 

In reply to SVreX (Forum Supporter) :

I want to make sure the drywall and lumber I have is big enough to enclose the pipe that goes from the basement to the roof. I really don't  want to buy a $700 2x4 if I don't have to.

In reply to Appleseed :

OK, but I think you are asking the wrong question...

If the perpendicular of your triangle is 4.5" and 4.5"is  the outside diameter of your pipe, it won't fit in the triangle.  You need a triangle whose legs can encompass a 4.5" diameter circle.  That's not the perpendicular line.

And why are you making the pipe chase triangular?  Isn't it easier to square it off?

It's so much easier to lay this out as a practical "without" the math.

One more problem...

PVC pipe is 4.5".  But the hubs and fittings are not.  The hub of a 4" pipe is 5", not 4.5".  If you have any joints or fittings at all in this chase, your pipe won't fit.

I know you are trying to save precious 2x4, but you are not giving yourself any tolerances. 

You can build a very adequate pipe chase with NO 2x4's.  2 faces of drywall with a 1x1 cleat on the backside in the corner is sufficient.  It can also be done with no wood at all- just a sheet metal angle on the back corner of the drywall and metal drywall screws.

I can name 20 ways to build a pipe chase that don't include any math! Haha!

jgrewe said:

The pipe isn't going to reach all the way into to 90* angled corner so your dimension isn't 4.5".  More math needed or just throw the pipe into a corner and see how far it sticks out.

this.

(just showing the problem, I agree with svrex here)

You guys really need to go back and get a refresher in your geometry...

Make trial templates from pizza or beer boxes. 

In reply to SVreX (Forum Supporter) :

E36 M3, coupler OD size.  This is why I ask things like this. That's an important thing I overlooked.  I'm just going to use Ed's pizza box idea. 

YES!  

Ed and his pizza boxes for the win!

In reply to Appleseed :

One more thing...

Trust me on this.  If you try to save pennies of wood by calculating this chase so closely with ZERO tolerances, you WILL be building it twice.  I'm not trying to be an ass, I'm just trying to help you benefit from my 44 years of construction experience.  It NEVER goes together as easily as the engineers can draw it.  You HAVE to include tolerances.

Do yourself a favor... Make it a little bigger so you don't have to worry about it later.

AngryCorvair (Forum Supporter) said:

mtn said:

If I'm understanding this correctly, your hypotenuse is 9. In this picture, you're trying to find Y, right?

 

When you cut an isosceles right triangle in half from the right angle, you get another, smaller isosceles right triangle.

 

If you want more detail, as I skipped a step or two in this "proof"  here, happy to give it in the morning. 

Your proof is flawed. In your pic, x^2 + x^2 = 81, not 9. 

That's what I get for trying to do math at 1:30am. 

SVreX (Forum Supporter) said:

In reply to Appleseed :

One more thing...

Trust me on this.  If you try to save pennies of wood by calculating this chase so closely with ZERO tolerances, you WILL be building it twice.  I'm not trying to be an ass, I'm just trying to help you benefit from my 44 years of construction experience.  It NEVER goes together as easily as the engineers can draw it.  You HAVE to include tolerances.

Do yourself a favor... Make it a little bigger so you don't have to worry about it later.

Oh, trust me, I've paid the price forgetting the saw takes an 8th every cut.