I need a little math help.

[Rich Engelhardt]

http://emweb.unl.edu/math/mathweb/trigonom/Image289.gif

If "C" is 3 inches, what's the length of "a"?
What's the length of "b"?

a,b is 90 degrees.
What's the angle of a,c ?
What's the angle of b, c?

This is for some trim I need to install. Imagine rotating the triangle so that "a" is the wall surface. The trim, which is "c" is 3". I need to joint or cut the bottom of the trim "c" at the proper angle on the top (where b,c come together) and the bottom (where c, a come together).

I'm a bit lost here - it's been a long time since HS geometry.

[Stephen Cherry]

Rich, it's been a while for me also, but I think you need to know one more length or angle to get the answers.

[Dave Wagner]

If you do Google Search...but I believe you need 1 more value, either a side or another angle to solve. You can't get there form here unless you make an assumption for the another angle. Your 3" and 90 Deg. can remain the same, but if you move it up or down, the other angles will change.

http://www.csgnetwork.com/righttricalc.html

[John Coloccia]

You need to know more information.

For example, the angle between C and A, or the angle between A and B would be useful. If you call the angle between C and A Tca, and the one between C and B Tcb, these relationships tumble out.

B = C * sin(Tca)
A = C * sin(Tcb)

So you need to define one of the other angles first, and everything else will tumble out. You can see that by changing the angles, a ling segment of length C can make an infinite number of different right triangles.

[Bill Orbine]

You need one more value (Angle AC or BC or Length A or B or some other point of reference) other than length of C and the angle of AB to summarize the triangle. Why not test with scrap wood rather than do the math?

[Shawn Pixley]

As others have said. You need another value (angle or length) to determine anything else. After that, it will be very easy. To get all other values.

[David Nelson1]

If C= 3.0 inchs. Draw A then set a compass or tremel to 3 inches. Draw an arch or just mark the spot from left to right above line A. Using as square draw a 90* line from A to create line B. Lay a drafting protactor on line A till you have found the angle.

Disclaimer: I might be totally wrong but I got 2.5 +/- .010 for A. B came out to 1.481 and the and was about 30*

Hope thisis right and it helps LOL

[Mike Barney Sr]

With a 90 degree triangle you need to know the length of 2 sides, or the length of a side and an angle (besides the 90). Then you can figure out the rest using pythagorean's theorem (a^2 + b^2 = c^2) or sine, cosine, etc. Knowing just the hypotenuse and the 90, the remaining 2 angles could be anything, although they will total 90 degrees.

Take a square and rest the trim against the inside at the angle you want. Then measure the distance from the inside corner to the inside surface of the trim ("b" in your drawing). On your scientific calculators you will see the sine button as sin. Above it (the second function) is sine to the power of -1. Divide the side by the hypotenuse. This is the ratio of the side to the hypotenuse. press the 2nd function key then the sin key and the angle is displayed.

For example if b is 2" then angle ab is:

c / b = 2 / 3 = .666

sine^-1 .666 = 41.8 degrees

Hope this helps.

[David Nelson1]

I agree that more info could have been helpful. Knowing the intersecting angles of A and B which where 90* You figure out the other lenghts form the info provided. I'm no smart guy but this seems reasonable to me.

[James Phillips]

The problem is under constrained. You can work out a "set" of possible solutions. Based one your description of the tasks pick a value for a (or b, or one of the angles) then use the law of sines to solve for the unknowns. I think any of the solution sets will work, you just have to decide what looks best

[David Nelson1]

I went to that calculator and pretty much came up with the same answer I gave earlier. The only thing I forgot was that the 3 inch line has no angle its just a line. Angles AC is 30* the other is 60* relative to the 90* angle plus or minus a bit due to my eyesight. Calculator is neat but not needed IMO

[Bill Huber]

I went to that calculator and pretty much came up with the same answer I gave earlier. The only thing I forgot was that the 3 inch line has no angle its just a line. Angles AC is 30* the other is 60* relative to the 90* angle plus or minus a bit due to my eyesight. Calculator is neat but not needed IMO

But could not the angle AC be 20 and the other one be 70?

We do not know what the length of A or B is, it could be anything. The only thing we know is C=3 inches and angle AB is 90, that means the other 2 have to equal 90 degrees but that could be any combination of angles.

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[David Nelson1]

I stand corrected! Dag nabbit Muskey. Actually if I had got the compass out instead of a veneer calipier I might have realised it wasn't that simple. Thanks for straightening me out Bill.

[Eiji Fuller]

I always just go to handymath.com

[Bill Huber]

I always just go to handymath.com

Great link, I have that one bookmarked, thanks.
But it won't help with Rich's problem.

[Chris Padilla]

Is this crown molding? If so, they are typically cut at standard angles:

http://www.altereagle.com/Crown_molding.html show the two most popular cuts.


With any math problem, the number of unknowns must equal the number of equations or you cannot fully solve the problem. In a triangle, you must know 3 of any combination of angles or side lengths to completely solve all unknowns.

So if you can find another term, you can solve your problem. While I'm only too happy to sit down and grind out math for my ww'ing, I'm finding that eyeballing stuff or marking to cut is usually easier, faster, and less prone to mistakes.

Just eyeball it and make some test cuts to get the fit you want.

[Roger Bullock]

If this was a theoretical problem, I would agree with the rest that you will have to have another known to figure the rest of the missing lengths and/or angles. But this is a physical problem meaning it is actually there (your wall). If you know either your starting point or ending point, make a mark on the wall measure back to the 90 degree corner and you have your other variable to complete the equation.

[Steve Costa]

You trig guys are very very good!!!! My math life stopped at geomerty!!!!

Pythagoras figured this out a long time ago.
A (squared) + b (squared) = c (squared)
Angles for a right triangle, if this is what it is, are 30, 60 90 degrees.

So: measure either A or B & plugin as follows:
So let us say A = 4" & C = 3"

4 squared + 3 squared = b squared
16 + 9 = 25 = b squared
b= the square root of 25 which = 5

If it is not a right triangle...such is life.

[Keith Hankins]

Well, if you have excel I know solver will solve a similtanious equation which this is. I just need to figure how to put the equation in to make it work. I'll play with it and see if I can get it to come out.

Update =

Ok it took me a bit but if I plugged the formula in right for solver, if side c the hypotinus is 3 and this is a rt triangle then side a = 2.212 (actually about 8 decimal points longer but rounding to 2 places is good enough) and B= the same. I had to put in a constraint and chose that side a and b were greater than 1.

[Chris Padilla]

Well, if you have excel I know solver will solve a similtanious equation which this is. I just need to figure how to put the equation in to make it work. I'll play with it and see if I can get it to come out.

Update =

Ok it took me a bit but if I plugged the formula in right for solver, if side c the hypotinus is 3 and this is a rt triangle then side a = 2.212 (actually about 8 decimal points longer but rounding to 2 places is good enough) and B= the same. I had to put in a constraint and chose that side a and b were greater than 1.

Keith,

You assumed that the two unknown angles are the same or 45 degrees each. If true, then the sides are simply 3/sqrt(2) = 2.121.

[Rich Engelhardt]

Thanks!
I'll have to play around with it and see what looks best.

This:
http://www.csgnetwork.com/righttricalc.html

gives me a good starting point.

We had sliding replacement windows put in & the sills (stoops?) need replaced. The replacement windows aren't inset into the wall anymore like the old windows were. I only have roughy 1/4" of space between the sides of the windows and the wall surface.
My idea is to put up a nailer - similar to hanging crown - so there's something for the sill (stoop?) to sit on that's wide enough to support it.
Then I'm planning on boxing in the nailer with some of the same trim I use around the windows.

[Keith Hankins]

Keith,

You assumed that the two unknown angles are the same or 45 degrees each. If true, then the sides are simply 3/sqrt(2) = 2.121.

Based on the picture on the original post you are correct. I assumed a rt triangle and used the pythagorean theorem as my forumla. It's amazing what you remember from college(or in my case half remember). When I saw this post I remember solving for multiunknown variables and how sweet excel is for that.

[Paul Saffold]

This one is pretty easy to use.
http://ostermiller.org/calc/triangle.html

[Rick Moyer]

I may be misunderstanding what it really is you need to do, but if you are talking about "c" being crown molding and you need it to sit flat against the wall and ceiling, the typical angles are 38 and 52 degrees. (see here http://www.altereagle.com/Crown_molding.html). Otherwise, all the Pythagorean theorum and trigonometry won't work without at least one more side dimension or one more known angle, as stated already.

[Chip Lindley]

Sometimes geometry is useless after rough carpenters frame a dwelling. And, the drywall men do their thing!

Should you find an exact 90 degree angle in a structure, you're just lucky. For that reason, I cut to the chase and use an adjustable square to copy the angle. That angle can be measured with a protractor, and divided in half if necessary, for miters. For larger work, simply mark the exact angle on a strip of ply or board held against one surface, with another piece of straight board on the opposite surface, as in the angle of rise of a staircase.

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[Nick Laeder]

There are no magic buttons. No piece of software can come up with a solution to the problem without more information. Bill Huber shows why, graphically. It's the exact same thing as trying to solve x + y + z = 6. If x=2, what are y and z? Impossible to solve without making assumptions.

There have been a ton of assumptions made, from assuming that a right triangle is always a 30/60/90 triangle to assuming that both legs are the same length, giving a 45/45/90 triangle. Right triangles also include 31/59/90 triangles and 30.1/59.9/90 triangles and 10/80/90 triangles, and everything in between.

The best advice I've seen here is to go to the wall, make a mark where you want one end of the 3" trim to fall, and measure from there to the corner of the wall/ceiling. Then, you have your other piece of information, and the math becomes simple.

[Russ Filtz]

I'm an engineer and deal with math every day, so I'm LOL'ing at all the discussion. I'm just glad a few of you are spot on!