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Lawsof Sines - Example 4

In trigonometry, the law of sines, also called the law of sines, is a trigonometric identity relating the sides of a triangle to the lengths of its three angles. The law of sines is a special case of the law of cosines, since cos(A) = sin(A) / sin(A).

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thing. Sides and missing angles using trigonometry functions for Triangle ABC. Where angle see, it's 75 degrees Side A is two units and see it's three units now because I only know one angle. I can't go ahead and just subtract from 1 80 to find my ankle. So instead we're gonna set this up as a proportion. So let's start by finding Let's just start with angle A So we're gonna find sign of a over side A will equal sign a C over sazi. Now, we don't know Sign of a so we'll leave that sign of a But we do know the length of Side A which is gonna be too. We also know that angle. See, it's 75. So we're gonna find Sign of 75 and side CS three. So we're gonna cross multiply, so we're gonna have to. Tom's son of 75 will equal three Tom's son off a now this one because we're looking for sign of a we're gonna divide both sides by three. So that would give me when I round to sign of 75. That's gonna give me approximately 1.932 and we'll divide that by three. And that should give me a sign of a So when I do that, I'm gonna get in approximate value of 0.644 would be the son of a So when I do the reverse operation in my calculator, that's going to mean that angle A is going to be approximately 40 degrees. Now that we know that we can go ahead and we can also do the same to find, um, are missing shots. So now that we know are two lengths, we can go ahead and we snow that angle a plus angle B plus angle c equals 1 80. Well, now, even though we've gotten approximate, we're gonna go ahead and put 40 for a We don't know be, but we do not see a 75. So that's going to give me 115 plus B would be 1 85 1 80. So when I subtract, um 1 15 from 1 80 I can see that angle be. We're gonna go ahead and say approximately because again that 40 is an approximate. So we're gonna say be isas. Well, 65 degrees. So now that we know that we can go ahead and find side B. So we're gonna use son, be over sod be, will equal son See over side. See, signed. Be. Since we know that angle is now 65 we're going to sign a 65 over side B. And we were told that angle see is 75 side see is three. So we're gonna cross multiply, so we're gonna be a sign of 75 is going to equal three. Sign of 65. And since we're searching for B, we're going to divide by son of 75 on both sides. That's gonna leave me with B equals three times. Sign of 65 is approximately 2.719 and sign of 75 0.966 And when I divide that, that gives me an approximate value of 2.8. So that tells me that Side B is approximately 2.8

Liberty University
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