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Joshua has a ladder that is 25 ft long. He wants to lean the ladder against a vertical wall. Because of some plants next to the wall, the bottom of the ladder will need to be at least 5 ft away from the wall. For safety reasons, he doesn't want the angle the ground makes with the ladder to be more than 75 degrees. Find the angle between the ladder and the ladder and ground if placing the bottom of the ladder 5 ft from the wall. If this is unsafe, find the number of feet away from the wall that the bottom of the ladder should be place to have an angle at 75 degrees and be safe. Show all your work and draw a diagram to support your answer.

 Apr 9, 2019
 #1
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We can use the cosine inverse to find the angle

 

cos (theta)  = 5 / 25   = 1 / 5

 

So

 

arccos (1/5 ) = theta  ≈  78.5°......this is unsafe 

 

To find the safe distance, D.....we can solve this

 

cos 75  =  D  / 25          multiply both sides by  25

 

25 * cos 75  ≈  6.47 ft ≈  6.5 ft = D

 

 

cool cool cool

 
 Apr 10, 2019

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