SOLUTION: Companies like AT&T charge corporations additional fees for private networks between office locations. The fee is based on the minimum number of feet of cable used to connect the l

Question 174980: Companies like AT&T charge corporations additional fees for private networks between office locations. The fee is based on the minimum number of feet of cable used to connect the locations.At one time in the past, Delta Airlines had three main office locations, which roughly formed an equilateral triangle. The offices are labeled A, B, and C in the diagram, and there are lines connecting A to B and B to C, but not A to C. The line segments represent the best way to connect the cables. Delta wondered if there was a way to use less, so they hired a mathmetician to figure out a way to do so. The mathmetician determined that the best way is to create a cable junction directly in the middle of the equilateral triangle because it would save a lot. This diagram has the points A, B, and C in the same position, but no lines between them; instead there is a point D marking the exact middle of the triangle. From this there is segment AD, BD, and CD, slightly resembling a peace sign without the circle. Given this information, by what percent was the amount of cable reduced by creating a cable junction?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Companies like AT&T charge corporations additional fees for private networks between office locations. The fee is based on the minimum number of feet of cable used to connect the locations.At one time in the past, Delta Airlines had three main office locations, which roughly formed an equilateral triangle. The offices are labeled A, B, and C in the diagram, and there are lines connecting A to B and B to C, but not A to C. The line segments represent the best way to connect the cables. Delta wondered if there was a way to use less, so they hired a mathmetician to figure out a way to do so. The mathmetician determined that the best way is to create a cable junction directly in the middle of the equilateral triangle because it would save a lot. This diagram has the points A, B, and C in the same position, but no lines between them; instead there is a point D marking the exact middle of the triangle. From this there is segment AD, BD, and CD, slightly resembling a peace sign without the circle. Given this information, by what percent was the amount of cable reduced by creating a cable junction?
:
You can use the law of sines to find the length of the segments AD,BD,CD
The triangles formed by the lines to D have angles 30,120,30
Assume that distance AB and BC = 10, then find AD
=
Cross multiply:
.866(AD) = .5(10)
AD =
AD = 5.77 * 3 = 17.32 total cable required to the junction
:
2 * 10 = 20 original total cable distance
:
20 - 17.32 = 2.68 less cable
:
= .134 or 13.4% reduction in cable
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