A 20 m ladder and a 15 m ladder were leaned against a building. The bottom of the longer ladder was 7 m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find the distance.

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A 20 m ladder and a 15 m ladder were leaned against a building. The bottom of the longer ladder was 7 m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find the distance.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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i think its 12 let me show you my picture. first let me draw it better k?
ok
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Other answers:

smurfy what do you think?
it helps! except the bottom is cutoff..do you think you could repost the bottom part?
it just says what h=sqrt{225-81}=sqrt{144}=12
i'm painting my nails
haha nice and oh ok thanks a bunch!
if you call the angle between the ladders x then by law of cosines cos(x)=.8 making sin(x)=.6 and therefore the height is 20*.6=12 which i think was already given as an answer yes?
np
i win satellitle
i know i am slow
satellite73 ya i know but i dont get the whole cos sin thing and this makes more sense
ahhh no trig for this one?
did my without law of cosines so you came up with a differnet way gj
oh i see your picture. which might in fact be essentially how one proves the law of cosines!
good work
maybe
i might check tht out later how to prove that
kinda quiet tonight. maybe it is break time
smurfy check the other post you made of this I did it a simpler way
if you on break i might catch up with you
i think that is inevitable.
lol
simpler than the law of cosines version i mean
oh let me see!
i can help 200 people
rbsitale did you see my way?
when you get to 1000 they will send you a bicycle
no way
let me look at yours one sec
haha rb ya thats way easier than ur previous way :P
*rsvitale not rb lol
yes myininaya thats the way i did it the second time I wasnt thinking and used law of cosines first
oh yay great minds think alike
satellitle is brillant too :)
good I like mathematicians haha
have you seen any of watchmath's problems he posts some interesting ones here.
the calculus dream problem i got close on it i think
i havent seen that one. I did a few of his others though and they were pretty fun.
doing my nails is so hard
i want to put an orange pi symbol on all of them after painting them blue
haha that would be cool
don't think it will work
Ive never seen anyone do that
take a exacto knife and cut out a small pi stencil then stencil it on
an*
i need more finite space on my nails
okay if it works i will post my nails on here later
up for helping me with another word problem??
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i will try to help with one hand
ok and ill brb
ok im back!
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hope smurfy gets the idea of the solution
thanks mark; myin how did you break x^2-48x+560 at the end to get the whole -20 stuff???
we had 48=x+560/x i multyplied by x on both sides
do the law of hypotenuse: c^2 = a^2 + b^2 here the height is C, the base is b , and the opposite sides are 15 and 20 c^2 = 20^2 +(7+x)^2 the other one is c^2 = 15^2 + x^2 now equate them together c^2=c^2 we get 20^2 +(7+x)^2=15^2 + x^2 do the little algebra 20^2 - 15^2 + (7^2 +2*7*x)+x^2=x^2 cancel the x^2 175 + 49 +14x=0 oh here it is 14x=224 x=24/14 x=16 answer
in the end you went from x(x-20)-28(x-20)=0 to (x-20)(x-28)=0 how did you know to di that?
*do
mark its a rectangle so if ur right you need another answer
i just factor the long way we have x^2-48x+560=0 if you want you can use the quadratic formula or find factors of 560 that add up to be -48 so we have (x-28)(x-20)=0
oh alrighty thanks!
lol you like totally get it?
ya i do!! :)
ok wish me luck on my nails?
any luck with your answer yet?..lol
good luck and have fun! you should attach a picture to this question when youre done and ill check it out :)
lol k
the answer is x= -16.. you can check it by doing the hypotenuse law c^2= a^2 +b^2 c^2= 15^2 +(-16)^2=481 the other one is c^2= 20^2 +(7-16)^2=481 checked

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