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MATHEMATICS - CASE STUDY

    Introduction



The State of the Ladder
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In order to hang a painting on a well, Jim moved a ladder and leaned it against the wall. However, the ladder started to slide away from the wall when he started clim the ladder.

What is known:

  • The length of the ladder is 12 ft.
  • The ladder horizontal speed at the base is 3 ft/s.
  • The distance between the bottom of the ladder and the base of the wall is 8 ft.
    Questions


Simplified Ladder State


 

How fast does the angle, θ, between the ladder and the wall change when the bottom of the ladder is 8 ft from the base of the wall?

   
  Approach

  Using the inverse trigonometric function to calculate the rate of change of the angle θ.