January 21, 2017

Homework Help: Calculus

Posted by CMM on Wednesday, March 23, 2011 at 12:39am.

A 24 foot ladder is leaning against a building. Let x be the distance between the bottom of the ladder and the building and let theta be the angle between the ladder and the ground.

a)Express theta as a function of x.

cos theta = x/24
theta = arccos(x/24) correct/incorrect?

b)When the angle is 40 degrees (2 Pi/9 radians) how big is x?

40 degrees = arccos(x/24)
cos(40 deg.)= cos(arccos)(x/24)
x= 18.385 feet coorect/incorrect?

c)Suppose the bottom of the ladder is sliding away from the wall at a rate of 2 ft/sec. When x=6, how fast is theta(in radians/sec.) changing?

I really don't know about this last part... help/hints would be greatly appreciated! Seems sort of like a physics problem.

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