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Imagine for a moment a scene in a bank where a man threatens to shoot everyone dead Imagine the criminal doesn't know about two of the hostages In this sense, they are the only ones who can run outside and go for help For now, let's call them A and B For a moment let's forget about the criminal and just consider A and B They might not know it but WE know that between one another, is a distance of 5 meters that they form an angle of 81° with the door and that A is at 3.45 meters from the door Now, if for a moment we say both of them run at the same speed do you know which one has the best opportunity to run outside before the man can shoot them? I guess the logic answer would be "does that even matter, just run for it!" or "why don't you just use your cellphone and call the police?" BUT because this is math, let's unnecessarily complicate things For this case, we'll use the LAW OF SINE In trigonometry, the law of sine is an equation relating the lenghts of the sides of any shaped triangle to the sines of its angles So, according to this law in order to calculate lengths, we use a/sinA = b/sinB = c/sinC And to calculate angles, we use sinA/a = sinB/b = sinC/c Where the lower case refers to the lengths and the upper case refers to the angles So in order to answer the question and know who has a better opportunity of surviving and to explain completely this law Let's first search for the rest of the triangle's angles So, if we have that sinB/b = sinC/c then sinB/3.45m = sin81°/5m Let's go step by step sinB converts to sinB = (sin81°/5m)3.45m which s equal to 0.68 And to have B alone, we convert it to B = sine inverse of (0.68) Which results in 42.96°, but to make it simpler, let's round it to 43° And because I'm assuming that we all know by now that the addition of the internal angles of a triangle gives us a total of 180° we can just add 81° plus 43°, equal to 124° and then subtract the result from 180 this way we'll get A's angle, equal to 56° From here, the only thing left is to calculate the distance between B and the door which we do by comparing a/sinA = c/sinC that will be the same as saying a/sin56° = 5m/sin81° This will convert to a = (5m/sin81°)sin56° which gives us as result 4.19 meters Se, we determine that A is the one who actually has a better chance of running out alive *SHOTGUN FIRES* but I guess we'll never know if they made it

Video Details

Duration: 3 minutes and 35 seconds
Year: 2015
Country: Mexico
Language: English
License: Dotsub - Standard License
Producer: me
Director: me again
Views: 54
Posted by: kacesa on Nov 18, 2015

1213, Karen Centella #512468, 3RD SEMESTER

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