trigo with some derivatives?help!!!!!me?

Question

Finf the length of the shortest ladder which will reach from the ground level to a high vertical wall if it must clear an 8ft vertical fence which is 27ft from the wall.

umm i mean calculus with dervatives

Answer 1

There are two ways of doing it. The easier one would be using the hypothenus law.
27^2+8^2= square root 793
= 28.16ft.

The hard way would be using the sin or cos law. But I do not know how. LOL

I hope this helps.:)

Answer 2

the length of the ladder is l. the ladder touches the 8 ft wall and is divided in l1(before the wall) and l2 after the wall. the angle between the ladder and the ground is a.
l=l1+l2= 8/sin(a) +27/cos(a).
to get a minimum of the lenght the derivate of the function l(a) must be 0.
l'(a)=8*cos(a)/sin^2(a)-27*sin(a)/cos^2(a)=0
8cos^3(a)-27sin^3(a)=0
8/27=sin^3(a)/cos^3(a)=tan^3(a)
tan (a)=2/3
a=33.69
l=8/sin(a)+27/cos(a)=46.87