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# 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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##### Top Educators ##### Alisa L.

University of Texas at Austin ##### Boris M.

University of North Carolina at Chapel Hill ##### Martha R.

Michigan State University ##### Kristen K.

University of Michigan - Ann Arbor

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minds to find the missing angles and sides of Triangle ABC. Where angle a equals 59 degrees angle. B. It's 48 degrees inside. C is 62 units. Let's go ahead and find our angle. See, now we know in a triangle, but the three angles and got a B and C all add up to give me 180. I know angle A is 59 degrees and I know angle B S 48 so we can use that information to find angle. See, 59 plus 48 is 107. So when I subtract 1 80 107 from 1 80 that tells me that angle beat angle See, excuse me, is going to be 73 degrees. So now that I know angle see, we can go ahead and we can find our missing sites. So now we know angle see, And we know the side for C. So that's gonna be the fraction we're gonna use each time. So let's start with sign of c, the volley by sea and let's go ahead and find a So will you sign of angle a divided by Saturday. So for this one We know that sign of C is 73 degrees and we know that side See is 62. We also know that angle A. He is 59 so we can go ahead and put that in for son of 59 and we don't know, side A. So we're gonna cross multiply, so we'll have 60 to Tom's son of 59 will equal a time sign of 73. Since we're solving for a we're gonna go ahead and divide both sides by son of 73. So that will leave me with a equals 62 sign of 59 which will round 2 53.144 over Sign of 73 is 0.956 And when I divide those two values, I'm gonna get an approximate answer a 55.6. So that tells me that Side A is approximately 55.6. So now we can find that Use that to find angle be our side bay. So saint sign of C divided by C will equal sign of B divided by Assad Bey. So we already know that sign of C is angle. See? Is 73 degrees and we know that side See is 62. We know that angle B. It's 48. We'll have sign of 48 over B and we'll cross multiply, so we'll have 62. Son Ah, 48 will equal be son of 73. We'll divide by sign of 73 on both sides because we're gonna be solving for B. So that leaves me Would be will equal 62 signs of 48 is gonna be approximately 46 0.75 and sign of 73 0.956 And when I divide, those are getting approximate value of 48.2. So that tells me that side B is approximately 48 point to Liberty University

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Graphing Trigonometry Functions

##### Top Algebra 2 Educators ##### Alisa L.

University of Texas at Austin ##### Boris M.

University of North Carolina at Chapel Hill ##### Martha R.

Michigan State University ##### Kristen K.

University of Michigan - Ann Arbor