Question

A ladder, 10 ft long, rests against a wall. If the bottom of the ladder slides away from the wall at 2 ft/sec, how fast is the angle between the top of the ladder and the wall changing when the angle is 45 degrees?

Answer 1

can you write \(\theta\) in terms of x?

Answer 2

\[\sin \Theta=\frac{ x }{ 10 }\]
\[x=\sin \Theta \times10\]

Answer 3

now differentiate both sides with respect to 't'

Answer 4

\[\frac{ dx }{ dt }=\cos \theta \times \frac{ d \theta }{ dt }(10)\]

Answer 5

read the question
you are given,dx/dt and the angle theta=45
substitute

Answer 6

Oh ok! \[100=\cos(45)\times10(\frac{ d \theta }{ dt }\]

Answer 7

So all that's left is solve for the derivative of theta?

Answer 8

dx/dt=2 ft/sec
re-check, how did u get 100?

Answer 9

Oh, my bad. I was looking at the wrong value. Saw the 10 ft in the problem and for some reason wrote 100

Answer 10

cos(45)=\(\frac{1}{\sqrt{2}}\)

Answer 11

substitute and find \(d\theta/dt\)

Answer 12

Ok, thank you for the help!

Answer 13

:)