# A fence(3m tall) parallel to the wall of a building and 1m from the building.What is the length of the shortest ladder that can be extend from the ground over the fence to the building wall?

Sep 16, 2015

the minimum length of ladder is 5.406m

#### Explanation:

answer is very simple . the length of the ladder which is to be caluclated must be minimum .

so the length of the ladder = 3*cosec (x)+sec(x)
applying derrivation on both sides gives the minimum length of ladder required

0= -3cosec(x)cot(x)+sec(x)tan(x)
that implies
${\tan}^{3} \left(x\right) = 3$
x=55.7 degrees

the minimumlength of the ladder is 3cosec(55.7)+sec(55.7) (in degrees)
the minimum length of the ladder is 5.406m