SOLUTION: Hello I have a word problem on the Pythagorean theorem. It says.... the bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground

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Question 829545: Hello I have a word problem on the Pythagorean theorem. It says.... the bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? I also need help like lets say a lawn is 4 meters by 5 meters... how much is it if you cross diagonally across I dont know how to solve both of these problems.. thanxs
Found 2 solutions by josmiceli, LinnW:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The legs of a right triangle are the 2 sides
that are 90 degrees to each other.
The 3rd side is the hypotenuse.
----------------------------
Let +a+ = one of the legs
Let +b+ = the other leg
Let +c+ = the hypotenuse
-------------------------
The pythagorean theorem says:
+a%5E2+%2B+b%5E2+=+c%5E2+
---------------------
For your problem, you can say +a+=+3+ ft
The length of the ladder is the hypotenuse,
so +c+=+12+ ft
----------------
The distance from the ground to where the ladder
touches the wall is +b+, so
+3%5E2+%2B+b%5E2+=+12%5E2+
+9+%2B+b%5E2+=+144+
+b%5E2+=+135+
+b+=+sqrt%28135%29+
+b+=+11.619+ ft
-----------------
check:
+a%5E2+%2B+b%5E2+=+c%5E2+
+a3%5E2+%2B+11.619%5E2+=+12%5E2+
+9+%2B+135.001+=+144+
+144.001+=+144+
close enough
----------------
Your other problem is
+4%5E2+%2B+5%5E2+=+c%5E2+
+16+%2B+25+=+c%5E2+
+c%5E2+=+41+
+c+=+sqrt%2841%29+
+c+=+6.403+ meters is the
diagonal distance



Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
For the ladder problem, the ladder is the hypotenuse.
Let h = height to the top of the ladder.
So h^2 + 3^2 = 12^2 , based on a%5E2+%2B+b%5E2+=+c%5E2
h^2 + 9 = 144
add -9 to each side.
h^2 = 135
take the square root of each side.
h+=+sqrt%28135%29
h = 11.62
___
For the lawn that is 4 by 5, the diagonal is the hypotenuse.
(c=length of diagonal)^2 = 4^2 + 5^2
c^2 = 16 + 25
c^2 = 41
c = sqrt%2841%29
c = 6.403
Check tutorLinnWilson.jimdo.com if you need help.