a math question to do with the length of one side of a triangle?

Question

ok lets see if i can explain this one,today at work(im a carpentar)i have a 2x6 wood at a lenght of 20 feet long on the ground(horizontally),lets call it AB!!then i have another 2x6 at the end standing straight up(vertically)lets call that BC.i must now put another piece of wood diagonally from CtoA.so how can i find that length of the last piece.so what i have is a structure that is the shape of an L(or a right angle)i want to find the length of the hypotenuse i think it is.i hpoe this makes sense!!please help

Answer 1

20^2 +x^2= y^2
where x=BC
y= AC

so y=AC= sqrt(400 +x^2)

after you measure BC, square it, add 400, then take the square root after adding 400.

Answer 2

You have to use the Pythagorean theorem, which only works for right triangles (a triangle with a right angle). The pythagorean theorem is as follows: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse (the largest side).
You know a and b; they are both 20 feet. Therefore,
20^2 + 20^2 = c^2
400 + 400 = c^2
800 = c^2
squareroot(800) = c
c = 28.28427125 feet

To convert that decimal to inches,
.28427125 * 12 = inches
= 3.41125 inches
.41125 approximately equals 4 / 10 = 2 /5.
So the length of your board would need to be 28 feet, 3 and 2/5 inches.

Answer 3

I assume the first two pieces of wood are both 20 feet long.

Since we are talking about wood planks with real thickness rather than idealized mathematical concepts, it matters how you join the pieces of wood together.

For example, if you just attached the second piece of wood BC to the end of AB, then the horizontal base would be 20 feet, 2 inches long.

On the other hand, if you cut both the AB and BC pieces of wood at an angle (beveled) so they both came together at a point, then the horizontal base is 20 feet long. I am assuming that all three joinings of planks are beveled to a point.

In the case they are beveled, use the Pythagorean Theorem:

AC² = AB² + BC² = 20² + 20² = 400 + 400 = 800
AC = √800 = 20√2 = 28.284271 ft = 28 ft, 3.411255 inches

Answer 4

A "carpenter", sure. But, to answer your question, it will somewhat depend on where you want the hypotenuse to end up. For example, do you want to just touch the L-shaped 2x6 or cover them fully. I'm sure others will post the pythagorean theorem(hypotenuse = square root of (side A*A + side B*B), but that deals with a line and may not give an accurate measure when taking into account the width of the boards. So, make sure to delete or add the nominal thickness of the board when applying the pythagorean theorem.

Answer 5

That is Pythagoras theorem. The sum of the square of each sides is equal to the square of the hypotenuse.
So, the first piece being 20, the square of that is 400. The other side (which you did not size, but assume it is say 15) would have a square of 225. 400 + 225 is 625. And the square root of this 625 would be the hypotenuse length, which in this case, would be 25.
It happens to be a round number, but do not count on this always happening, though.

Answer 6

For this problem it is possible to use the Pathagorean Thereom.
A^2 + B^2 = C^2
One side of your so-called triangle is 20, we'll call that A
Another side is also 20, we'll call that B
Now we can plug those values into the equation above and solve for C
20^2 + 20^2 = C^2
400 + 400 = C^2
800= C^2
C= 28.284
Your third piece of wood should be about 28.284 feet long.

Answer 7

If you join the two legs by making a 45 degree cut on each, then the two legs are equal.

hypotenuse = square root of (20*20 + 20*20).

If you join the legs without cutting the ends, then you have to add the thickness of the wood as the length of the other leg of the right triangle.

Answer 8

Hopefully, this answer will help you out. The answer can be solved using something called Pythagorean Theorem, or in literal meaning, a squared + b squared equals c squared. C squared is the side you're trying to find. So, take the length of the two sides you do have, square them, and add these results together. After that, take the resulting answer and find the square root of it. That shoud be the length of the side you're looking for.

Answer 9

The equation for answering your question is A-squared + B-squared = C-squared. So, using your example, AB is 20 feet long. Twenty squared is 400. You didn't mention what the length of BC is, but you would need to square that number also. So far, we have 400 + BC-squared = AC-squared. Once you have the length of BC, multiply that number by itself and add it to the 400. The result is AC-squared. To get the length of the final piece, take the square root of the sum (400 + BC-squared).

Answer 10

Use the pythagorean theorem.
If you gave the length of BC, I could give you the answer.
it will be AC=√)20^2+BC^2)=√(400+BC^2)