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- Elenathehomeschooler

Can someone help!
A handy man knows from experience that his 29-foot ladder rests in its most stable position when the distance of its base from a wall is 1 foot farther than the height it reaches up the wall.
1. Draw a diagram to represent this situation. Be sure to label all unknown values in the problem.
2. Write an equation that you can use to find the unknown lengths in this situation. This equation should come directly from the labels you used in your diagram.
3. How far up a wall does this ladder reach? Show your work.

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- Elenathehomeschooler

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- Vocaloid

|dw:1444344809146:dw|

- Vocaloid

use the pythagorean theorem to find x

- 31356

Just a reminder, the Pythagorean theorem is a^2+b^2=c^2

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- Elenathehomeschooler

@31356 can you help me all i have so far is |dw:1444345667230:dw| im stuck

- Elenathehomeschooler

@jim_thompson5910 can you help me

- jim_thompson5910

|dw:1444346208997:dw|
\[\Large a^2 + b^2 = c^2\]
\[\Large x^2 + (x+1)^2 = 29^2\]
\[\Large x^2 + \color{red}{(x+1)^2} = 841\]
\[\Large x^2 + \color{red}{(x+1)(x+1)} = 841\]
\[\Large x^2 + \color{red}{x^2+2x+1} = 841\]
\[\Large 2x^2+2x+1 = 841\]
Now get everything to one side and use the quadratic formula to find x

- Elenathehomeschooler

so put |dw:1444346934670:dw| in thr quadratic formula @jim_thompson5910

- jim_thompson5910

|dw:1444347129681:dw|

- jim_thompson5910

|dw:1444347161312:dw|

- jim_thompson5910

|dw:1444347184674:dw|

- jim_thompson5910

|dw:1444347206109:dw|

- Elenathehomeschooler

okay i got x=-22.5 or x=76 did i get it right? @jim_thompson5910

- jim_thompson5910

both are incorrect

- jim_thompson5910

2x^2 + 2x - 840 = 0
a = 2
b = 2
c = -840
\[\Large x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
\[\Large x=\frac{-2 \pm \sqrt{2^2-4*2*(-840)}}{2*2}\]
\[\Large x=\frac{-2 \pm \sqrt{6724}}{4}\]
\[\Large x=\frac{-2 \pm 82}{4}\]
\[\Large x=\frac{-2 + 82}{4} \ \text{ or } \ x=\frac{-2 - 82}{4}\]
\[\Large x=\frac{80}{4} \ \text{ or } \ x=\frac{-84}{4}\]
\[\Large x=20 \ \text{ or } \ x=-21\]

- jim_thompson5910

go back to Vocaloid's drawing
notice how x is a height or distance
we can't have negative distance, so x = -21 makes no sense. The only practical answer is x = 20

- Elenathehomeschooler

oh okay i noticed what i did wrong

- Elenathehomeschooler

for number 3 the ladder will reach 29ft. on the wall right @jim_thompson5910

- jim_thompson5910

29 isn't the vertical distance
29 is the length of the ladder

- jim_thompson5910

again, look back at Vocaloid's drawing

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