SOLUTION: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (a) What is the velocity of the

Algebra ->  Trigonometry-basics -> SOLUTION: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (a) What is the velocity of the      Log On


   

Question 1186843: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.
(a) What is the velocity of the top of the ladder when the base is given below?
15 feet away from the wall
20 feet away from the wall
24 feet away from the wall
(b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 20 feet from the wall.
(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 20 feet from the wall.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

a^2+b^2 =25^2
a sqrt(25^2-b^2)
a=sqrt(625-225) b=15
a=20
rate of sliding

a^2+b^2 =625
2a(da/dt) +2b(db/dt) =0
15(2)= -20(2)(db/dt)2 m/s slidinf rate of top of ladder
3/4 m/s sliding rate of top of ladder