Question

Pplease show you work! I cannot figure out the steps

A fence 10 ft high runs parallel to the wall of a house at a distance of 6 ft. Find the length of the shortest ladder that extends from the ground, over the fence, to the house. Assume the wall of the house is 20 ft high and the horizontal ground extends 25 ft from the fence. The length of the shortest ladder is ft. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)

Answer 1

Let DC=10ft

A ㅌ BE C

BC=6ft

Let CE=b

AB=a

In triangle ABE and DCE

a/6+b=10/b

a=(60+10b)/b

Let AE=L

L^2= a^2 + (b+6)^2

=((60+10b)/b)^2 +(b+6)^2

Differentiate

2L dL/db= 2(60+10b)/b(-60/b^2)+2(b+6)

=-120(60+10b)/b^3+2(b+6)

dL/dB=0

0=2(b+6)(1-600/b^3)

b=-6

b=600^(1/3)=8.434

L^2=((60+10*8.434)/8.434)^2+(8.434+6)^2

=292.897+208.34035=501.23735

L=22.3883