A 10ft ladder leans against a wall at an angle theta with the horizontal. The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at which x changes with respect to theta when theta=60*

Question

A 10ft ladder leans against a wall at an angle theta with the horizontal.  The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at which x changes with respect to theta when theta=60*

anonymous · Answer

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like this?

anonymous · Answer

if thats the case, the relationship between theta and x is sin(theta)=x/10
you need to find dx/d(theta)
multiply both sides by 10 to get 10sin(theta) = x
dx/d(theta) = 10cos(theta)
convert 60 degrees to radians
plug that number in for theta
thats your rate

babyslapmafro · Answer

yes just lke the drawing