A ladder 10 ft long leans against a wall. The bottom of the ladder is 6 ft from the the wall. How much would the lower end of the ladder have to be pulled away so that the top end would be pulled down by 2 ft?
Don`t just give me an answer, show me how you did it.
2007-02-24 07:59:02 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Ok, 10ft and 6ft are the two numbers we have. scythian1 is perfectly right. Yea it's pythagorus's theorum; we start with a hypothesis of 10 ft, and a side of 6ft. That makes the other side 8ft tall. So if we bring it down by 2ft then that makes the bottom/ground 8ft.
2007-02-24 08:02:41 · answer #1 · answered by Put_ya_mitts_up 4 · 0⤊ 2⤋
Ok, start off by drawing a diagram. You have a right triangle (a triangle with a 90 degree angle), with the bottom side (distance between the wall and the ladder) as 6 ft., and the ladder as 10 ft. Your wall is unknown.
You have two sides of a right triangle, and from here you use the pythagorean theorem, a^2 + b^2 = c^2, where a and b are the sides and c is the hypotenuse (the diagonal side that connects the other two sides that form the right angle). You have B and C, so set it up like a^2 + 6^2 = 10^2
which equals a^2 + 36 = 100 or a^2 = 64. Take the square root of 64, which is (plus or minus) 8, but since a length can't be negative, you through -8 out. So you have the side as 8.
For the second part of the question, you just draw another diagram and put the 8 in. If the ladder is lowered 2 feet, you still have a 10 foot long ladder, and against the wall, your height is (8-2) = 6.
If you plug it into the pythagorean theorem again, you see it's the same problem, and that the bottom part of the triangle will be equal to 8. meaning you subtract 6 (the original length) from 8 (the new length) and you get 2, the answer to how much you would have to pull the lower end of the ladder to pull the top down by two feet.
Hope this helped.
2007-02-24 16:17:45 · answer #2 · answered by lokenog 1 · 1⤊ 0⤋
Ok...here's the answer and how to do it...
you do the Pythagorean theorem
x^2+y^2=hypotenuse^2
so first solve for how much space the ladder is actually taking up on the wall...basically the tallness of the wall.
x^2+6^2=10^2
x=8
so the tallness of the wall on which the ladder is leaning on is 8ft.
now this is the logical thinking part where you realize that this is a trick question.
You know know that the measure of thewall part is 8 ft so subtract this by two . This equals 6. Then do the theorem again.
6^2+x^2=10^2
x=8...this is your new base.
8(new base) -6 (old base)=2
The answer is that it would have to be pulled back 2 ft.
2007-02-24 16:15:08 · answer #3 · answered by tutorgirl 2 · 1⤊ 0⤋
Its a right-angled triangle.
Pythagoras: The square of the hypotenuse is equal to the sum of the squares of the other two sides.
1:
Hypotenuse = 10'
Base = 6'
Height = h
10² = 6² + h²:...100 = 36 + h²:...100 - 36 = h²
64 = h² : h = â64 = 8' (height)
2:
Hyp: = 10'
Base = b
height = 8 - 2 = 6
10² = 6² + b²:...100 = 36 + b²:...100 - 36 = b²
64 = b² : b = â64 = 8' (Base)
The ladder had to be pulled out by 2 ft
2007-02-24 16:18:55 · answer #4 · answered by Norrie 7 · 0⤊ 0⤋
Use Pythagorean to figure out the height of the top of the ladder, which is 8 feet. If we reduce this by 2 feet, so that it's 6 feet, use Pythagorean again to figure out how far out the bottom of the ladder will be from the wall, which is 8 feet again, which is just a coincidence. So, the bottom of the ladder needs to be pulled another 2 feet away from where it was.
If you don't know the Pythagorean Theorem, I'll remind you:
a² + b² = c²
where a and b are the sides of a right triangle, and c is the long hypotenuse.
2007-02-24 16:06:17 · answer #5 · answered by Scythian1950 7 · 1⤊ 0⤋
a^2+b^2=c^2
a=the height b= the base "6ft" and c is the hypoteneuse 10 ft the units ft are not needed working these numbers
a^2 + 36 = 100
a^2=64
a=8
now to lower the height of the ladder by 2 feet just subtract 2 ft from eight ft and work your way back through the equation to solve for how much you need to add to six feet to balance the equation. do you need a hint on what the answer should be.
2007-02-24 16:22:27 · answer #6 · answered by U-98 6 · 0⤊ 0⤋
You have a right triangle
Height is vertical measurement
Base is horizontal measurement
Hypotenuse is 10
H^2 + 6^2 = 10^2
H^2 = 64
H = 8
If H is reduced by 2:
6^2 + (6 + x)^2 = 100
36 + 36 + 12x + x^2 = 100
x2 + 12x - 28 = 0
(x + 14)(x - 2) = 0
x = -14, 2
Discard negative root
2007-02-24 16:13:15 · answer #7 · answered by kindricko 7 · 1⤊ 0⤋
10/6 = 8/x 10x= 48
48 divided by 10= 4.8 the ladder would have to be pulled out another 4.8 feet in order to be pulled down 2 ft.
i think i did it right but i am not sure
2007-02-24 16:05:34 · answer #8 · answered by nikka 2 · 0⤊ 2⤋
My brain hurts thinking about it I really tryed to awnser this question.
2007-02-24 16:03:57 · answer #9 · answered by Anonymous · 2⤊ 3⤋
try it!
2007-02-24 16:06:38 · answer #10 · answered by ME!!!! 2 · 0⤊ 2⤋