I'm having serious problems solving this. Any help would be greatly appreciated.
I'm having serious problems solving this. Any help would be greatly appreciated.
a:
What u will have to do is find the length of the ladders in the small triangles. So try to get the length of the ladder on the left from ladder b and the length of the ladder on the right of ladder a. If u have these lengths u can "flip" them over and have a bigger triangle to solve the length of the ladder AB.
07Scripter
I mostly write private scripts
AB = b / cos(alpha) + a / sin(alpha)
Working on: Tithe Farmer
I'll have to refresh my math a bit :P It's been a while since i have had this kind of math :P
07Scripter
I mostly write private scripts
I didn't really find a solution, but maybe i can help you get some ideas.
So what i was thinking is if:
Simba Code:ladder DL = tan (z) * 13 ( tan (z) = DL/13)
ladder CL = tan (x) * 67 ( tan (x) = CL/67)
ladder AK = 13 + (tan (x) * 67)
ladder BK = 67 + (tan (z) * 13)
tan (x) = (tan (x) * 67)/(tan (z) * 13)
tan (z) = (tan (x) * (tan (x) *67))/13
And then differentiate the last formula?
It's been too long for me since i had this kind of math
Sorry that i couldn't help you more
07Scripter
I mostly write private scripts
thanks for the help however I still dont understand what to do
if it helps anyone trying to solve this the value of x is 30.06765413 and the length AB is 103.3647197 I got the answers because I ran out of time however I can re attempt the question it will just give me different numbers at the start so I am still looking for the solution to this.
Well what i tried to do is if u could get Angle z then you would be able to get DL. Since AB splits a 90 degree corner into z and x' (z-angle) you could also get CL. Then if u have those 2 u know what AK and BK is. Then simply use tan(x) = AK/BK and u would have had AB. But maybe i'm completely wrong...
07Scripter
I mostly write private scripts
just got home from class now. Still not got any further, I hate this type of question pretty much all other types of math im ok with
True this is some though math..
07Scripter
I mostly write private scripts
AB = 13/sin(x) + 67/sin(90 - x)
This is based on the assumption that the ladder must contact the corner and that neither 0 or 90 degrees is important.
Differentiate and find x where length is minimum. (Slope = 0)
On my calculator it would seem L_max is 103.36ft and x is 30.07
I can post more when Im not doing so from a phone.
-Bam Bam
Sorry I didn't get it done earlier
One of my professors today was boring me so I did your problem from memory.
I looked at it last night though and had no idea how to do it then lol :P
-Bam Bam
tan (y) = sin(y)/cos(y)
and x = 90-z, so tan(z) = sin(90-x)/cos(90-x) = cos(x)/sin(x) = 1/tan(x)
the angle z depends on angle x, you wouldn't get that far with it. you need to express length of ladder as function of x then you can derivate
not to mention that the last two lines don't come out of first four lines.
here is how you do that:
n * sin(x) = a
m * cos(x) = b
n = a/sin(x)
m = b/cos(x)
so length as f(x) = n + m = a/sin(x) + b/cos(x)
derivate of 1/t(x) = -t'(x) / t^2(x)
so a/sin(x) derivate is -acos(x)/(sin(x)^2) and b/cos(x) derivate is bsin(x)/(cos(x)^2)
so you are looking for 0= a cos(x)^3 - b sin(x)^3, or after few adjustments:
tan(x)^3 = a/b
tan(x) = (a/b)^(1/3) (cubic root)
therefore x = approx 30.06
Edit: oops forgot the little drawing with m and n on it
Last edited by zmon; 05-22-2012 at 12:59 AM.
Perfect script? There is no such thing as "perfect", only "better than you expect".
i cant see the problem...
Try the cos-rule.
Angle = 30.06765414 Degrees
AB = 103.3647197 units
Will take a photo of my working in a sec and upload it, but it seems to be consistent with other people and your answer
Also post more things like this, maths problems are really fun imo
Last edited by putonajonny; 05-28-2012 at 05:53 PM.
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