document.write( "Question 1026693: a 10 inch book is leaning against a bookshelf when its bottom starts to slide away. By the time the bottom is 6 inches from the side of the bookshelf, the base of the book is moving at a rate of 3 in/sec. How fast is the angle theta changing at that time? \n" ); document.write( "
Algebra.Com's Answer #642179 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
a 10 inch book is leaning against a bookshelf when its bottom starts to slide away. By the time the bottom is 6 inches from the side of the bookshelf, the base of the book is moving at a rate of 3 in/sec. How fast is the angle theta changing at that time?
\n" ); document.write( "--------------------
\n" ); document.write( "You didn't spec where angle theta is, but the change will be the same regardless.
\n" ); document.write( "Using the bottom of the book that is on the shelf and the shelf as the angle and b as the side on the shelf and calling the angle A:
\n" ); document.write( "----
\n" ); document.write( "cos(A) = b/10
\n" ); document.write( "Differentiate wrt time.
\n" ); document.write( "-sin(A)*dA/dt = (db/dt)/10
\n" ); document.write( "sin(A)*(dA/dt) = -3/10
\n" ); document.write( "---
\n" ); document.write( "Side a = 8 inches
\n" ); document.write( "----
\n" ); document.write( "dA/dt = -3/(10*0.8)
\n" ); document.write( "dA/dt = -0.375 rad/sec\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );