How Do You Calculate Maximum Theta Between Two Buildings in Related Rates?

[kevinr]

[SOLVED] Related Rates - Sort of confused

Homework Statement

There are two buildings. One 20' high and other 40' high with a 60' distance between them. A person walking between them creates a theta with the buildings (see pic)

PICTURE: http://allyoucanupload.webshots.com/v/2003959771064888674

Now i am asked to find maximum theta possible if the person is walking 4ft/s to the left.

Homework Equations

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The Attempt at a Solution

I am kind of lost in coming up with the relation between theta and the two buildings. I know once i get the relation in terms of theta, i can take the derivative and find when the derivative = 0 and see if that's a max.

But any help with finding this equation would be greatly appreciated.

Thanks!

 

[HallsofIvy]

Are you sure that you have stated the problem correctly? The "maximum theta" will occur at a specific position no matter how fast the person is moving.

Let x be the distance the person is from the building on the right, in feet. Then the distance from the building on the left is 60- x.
Let \phi be the angle the line from the top of the building on the left to the person makes with the ground. Then tan(\phi)= 20/(60-x) so \phi= arctan(20/(60-x)).
Let \psi be the angle the line from the top of the building on the right to the person makes with the ground. Then tan(\psi)= 40/x so \psi= arctan(40/x). <br /> <br /> Of course, \theta is just \pi- \phi- \psi= \pi- arctan(20/(60-x))- arctan(40/x). To find the x that gives the maximum value for \theta, differentiate that and set equal to 0. <br /> <br /> Again, I don&#039;t see that how fast the person is walking has anything to do with that.

 

[kevinr]

o ok thx!