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  • Zipline
  • I haven been looking at the building across from my building for a while now and have been thinking of connecting a zip line to it but don't know how long it should be do you? 
  • Yes! Yes I do know how long this zip line wire should be. Good think I'm a Pre-Calculus  Wizard because it comes into play in situations like these.
  • Finding Accurate Length
  • My brother has asked me to do this for a long time now because he lives in the building across and doesn't feel like driving over every time, so I need and accurate length for the wire. 
  • I understand, and their are many of different trigonometry equations that can help us find this, each equation depends on which sides you are trying to find.
  • Numbers
  • Lets start talking about numbers The antenna of the building is 10 kilometers tall, and the angles are 34, 90, and 56. So we are trying to find the length of the blue line which is the wire so we will be using the Sine Equation which is Opposite over Hypotenuse. Blue=Hypotenuse, Opposite=Antenna, Angle=56
  • Ok Ok keep talking.
  • Usually people say math like this is never used anywhere but it very much can be used in problems exactly like this.
  • Beginning to Solve
  • So what we're going to do now is start plugging in the numbers, I have the numbers labeled for you so it shouldn't be to hard, Do you have what it takes?
  • Trig is a very good and effective way to to help someone find a missing length in this case of a right triangle.
  • Problem Solved
  • So if I Plug in the height of the antenna for the opposite length and 56 for the X i would get and equation of Sin(56)=10/Hypotenuse and when I FIgure out what Sin(56) is i multiply the right side by H (which is the hypotenuse)  and also the left side so it cancels on the right side and divide 10 by Sin(56) which is .83 I get 12.04 Kilometers as the Hypotenuse which is the length of the zipline wire.
  • Sine is being used in this case because we are using the connecting angle of the red line and blue line to find the hypotenuse by using the side length opposite of the angle which is the antenna and using the angle which is 56 degrees. Sin(x)=Opposite/Hypotenuse.
  • FInally ZIplining
  • Here comes my brother thanks so much Precalculus wizard.
  • Usually doing problems like this are not so easy to do without a calculator so having one handy will be good.
  • I think i can do this the only thing is I definitely need a calculator
  • These problems can get difficult but once you get used to them and have a bunch of them done under your belt it should be a breeze when you see these problems just like it was for Mr.Greenshirt.
  • The math worked and the brother finally was able to visit his brother without driving.
  • No Problem! Im always around so dont be araid to call me back here for other math 
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