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Lawsof Sines - Example 1

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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gods and angle of the triangle F G h. Using law signs just to kind of quick reviewed law signs, we set him up as proportions and we can see that sign of a divided by side a would equal sign of be divided by side B at which would equal sign a C divided by side. See before we go ahead, let's go ahead and find our missing angle. Were given two angles were given angle G and angle H and we just need to find angle f. Now we know in a triangle that angle F plus angle G plus angle age will equal 180 degrees. So in this one, we know we don't know elf, but we do know G is 80 and we know H is 40. And that all together is gonna equal 1 80 80 plus 40 is 1 20. So when I subtract 1 80 minus 1 20 I could see that angle elf is going to be 60 degrees because we can use that when we're finding are missing shots. So let's go ahead and let's start our first side. And since we're given, um, G, we're gonna use it is our main fraction. So we're gonna start off with sent sign of G over side G. And let's start with H So sign of H over side H. Now we know that sign of G is gonna be a sign of 40 because we know that G is 40 and we know that the side link I'm sorry of 80 not 40. And we know the side length of G is 14. We do know that H is 40 degrees so we can go ahead and put that a sign of 40. We just don't know side length of h. So now we've got a proportion. Let's cross multiply so we'll do Sign of 80 times. H will be h sign 80. We're equal. It's on 40 times 14. It's 14, son. 40. Since we're solving for H, we're gonna divide both sides by sign of 80 and that will cross out here and leave us with just a H on the left side. Now, I'm gonna go ahead and we're going to figure these out with calculator. You definitely wanna punch these in, and I'm gonna give you the round of values. 14. Sign of 40 would be approximately 8.999 and sign of 80 is approximately 0.9 85 And so the hell that we have that value we can divide and we're gonna get an approximate value of 9.1. So side H is approximately 9.1. So now let's fine sod if we're gonna keep this on G. So we're still gonna use San G over G. But this time we're gonna use sign elf over. If now, signed G is gonna keep what we've had. So we're gonna have son of 80 over 14. And we learned that, son, that elf iss 60 degrees. So we're gonna have a sign of 60 over if and so then we're gonna cross multiply. So we're gonna start off with Elf San 80 equal 14, Sign 60. We're gonna divide by son of 80 on both sides. So that leaves me on the left with elf 14 sign 60 is approximately 12.124 and sign of 80 is 0.985 which is gonna leave me an approximate value of 12.3. So we found that side F is approximately 12.3