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.

- smurfy14

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- schrodinger

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- myininaya

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

- smurfy14

ok

- myininaya

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- myininaya

smurfy what do you think?

- smurfy14

it helps! except the bottom is cutoff..do you think you could repost the bottom part?

- myininaya

it just says what h=sqrt{225-81}=sqrt{144}=12

- myininaya

i'm painting my nails

- smurfy14

haha nice and oh ok thanks a bunch!

- anonymous

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?

- myininaya

np

- myininaya

i win satellitle

- anonymous

i know i am slow

- smurfy14

satellite73 ya i know but i dont get the whole cos sin thing and this makes more sense

- anonymous

ahhh no trig for this one?

- myininaya

did my without law of cosines so you came up with a differnet way gj

- anonymous

oh i see your picture. which might in fact be essentially how one proves the law of cosines!

- anonymous

good work

- myininaya

maybe

- myininaya

i might check tht out later how to prove that

- anonymous

kinda quiet tonight. maybe it is break time

- anonymous

smurfy check the other post you made of this I did it a simpler way

- myininaya

if you on break i might catch up with you

- anonymous

i think that is inevitable.

- myininaya

lol

- anonymous

simpler than the law of cosines version i mean

- anonymous

oh let me see!

- myininaya

i can help 200 people

- myininaya

rbsitale did you see my way?

- anonymous

when you get to 1000 they will send you a bicycle

- myininaya

no way

- anonymous

let me look at yours one sec

- smurfy14

haha rb ya thats way easier than ur previous way :P

- smurfy14

*rsvitale not rb lol

- anonymous

yes myininaya thats the way i did it the second time I wasnt thinking and used law of cosines first

- myininaya

oh yay great minds think alike

- myininaya

satellitle is brillant too :)

- anonymous

good I like mathematicians haha

- anonymous

have you seen any of watchmath's problems he posts some interesting ones here.

- myininaya

the calculus dream problem
i got close on it i think

- anonymous

i havent seen that one. I did a few of his others though and they were pretty fun.

- myininaya

doing my nails is so hard

- myininaya

i want to put an orange pi symbol on all of them after painting them blue

- anonymous

haha that would be cool

- myininaya

don't think it will work

- anonymous

Ive never seen anyone do that

- anonymous

take a exacto knife and cut out a small pi stencil then stencil it on

- anonymous

an*

- myininaya

i need more finite space on my nails

- myininaya

okay if it works i will post my nails on here later

- smurfy14

up for helping me with another word problem??

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- myininaya

i will try to help with one hand

- smurfy14

ok and ill brb

- smurfy14

ok im back!

- myininaya

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- anonymous

hope smurfy gets the idea of the solution

- smurfy14

thanks mark; myin how did you break x^2-48x+560 at the end to get the whole -20 stuff???

- myininaya

we had 48=x+560/x
i multyplied by x on both sides

- anonymous

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

- smurfy14

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?

- smurfy14

*do

- smurfy14

mark its a rectangle so if ur right you need another answer

- myininaya

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

- smurfy14

oh alrighty thanks!

- myininaya

lol you like totally get it?

- smurfy14

ya i do!! :)

- myininaya

ok wish me luck on my nails?

- anonymous

any luck with your answer yet?..lol

- smurfy14

good luck and have fun! you should attach a picture to this question when youre done and ill check it out :)

- myininaya

lol k

- anonymous

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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