Can someone please help me solve this trig/calc problem?

Posted on 2016-04-29 18:41:00 in Math by EMLIY

The Y. O. Ming Construction Company is slated to build a new multilevel building in downtown New York City. All of the steel girders they are using to construct the building are 27 feet long. One of the corridors the girders are to be carried down has a 90-degree turn at the end. The width of the hall before the turn is 8 feet, and the width of the hall after the turn is to be determined. 
The owner of the building has instructed the lead architect of the construction company 
to make all the halls as close to 8 feet wide as possible, and no less. However, the 
architect, knowing trigonometry, figures out that the construction company's girders won't fit 
around the corner if the hall after the turn is 8 feet wide. Wishing to keep his job and the 
company's contract, the architect sets out to find the minimum width he can make the second 
part of the corridor to please the owner, while still making it possible for the Y. O. Ming 
Construction Company to carry the girders down the corridor. 

-The only problem is, the architect was more interested in designing houses than paying attention 
in his calculus class, so now he is turning to you to figure out how wide the hall should be. 
Assume the width of the girders is negligible. Show all work so the architect can understand your 
solution to his problem. 
-What is the longest the girders can be if the second part of the corridor is exactly 8 feet 
wide?

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