Question

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.

Answer 1

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

Answer 2

ok

Answer 3

smurfy what do you think?

Answer 4

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

Answer 5

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

Answer 6

i'm painting my nails

Answer 7

haha nice and oh ok thanks a bunch!

Answer 8

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?

Answer 9

np

Answer 10

i win satellitle

Answer 11

i know i am slow

Answer 12

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

Answer 13

ahhh no trig for this one?

Answer 14

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

Answer 15

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

Answer 16

good work

Answer 17

maybe

Answer 18

i might check tht out later how to prove that

Answer 19

kinda quiet tonight. maybe it is break time

Answer 20

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

Answer 21

if you on break i might catch up with you

Answer 22

i think that is inevitable.

Answer 23

lol

Answer 24

simpler than the law of cosines version i mean

Answer 25

oh let me see!

Answer 26

i can help 200 people

Answer 27

rbsitale did you see my way?

Answer 28

when you get to 1000 they will send you a bicycle

Answer 29

no way

Answer 30

let me look at yours one sec

Answer 31

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

Answer 32

*rsvitale not rb lol

Answer 33

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

Answer 34

oh yay great minds think alike

Answer 35

satellitle is brillant too :)

Answer 36

good I like mathematicians haha

Answer 37

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

Answer 38

the calculus dream problem
i got close on it i think

Answer 39

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

Answer 40

doing my nails is so hard

Answer 41

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

Answer 42

haha that would be cool

Answer 43

don't think it will work

Answer 44

Ive never seen anyone do that

Answer 45

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

Answer 46

an*

Answer 47

i need more finite space on my nails

Answer 48

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

Answer 49

up for helping me with another word problem??

Answer 50

i will try to help with one hand

Answer 51

ok and ill brb

Answer 52

ok im back!

Answer 53

hope smurfy gets the idea of the solution

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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?

Answer 58

*do

Answer 59

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

Answer 60

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

Answer 61

oh alrighty thanks!

Answer 62

lol you like totally get it?

Answer 63

ya i do!! :)

Answer 64

ok wish me luck on my nails?

Answer 65

any luck with your answer yet?..lol

Answer 66

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

Answer 67

lol k

Answer 68

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