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Determine whether the law of Then solve the sines or the law of cosines is needed to solve the triangle. triangle: Round your answer to threesdecimale B = 24.39,â...

Question

Determine whether the law of Then solve the sines or the law of cosines is needed to solve the triangle. triangle: Round your answer to threesdecimale B = 24.39,€ = 54.69 _ c = 2.68

Determine whether the law of Then solve the sines or the law of cosines is needed to solve the triangle. triangle: Round your answer to threesdecimale B = 24.39,€ = 54.69 _ c = 2.68



Answers

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. $$a=160, \quad B=12^{\circ}, \quad C=7^{\circ}$$

In this question, we've been asked to solve an oblique triangle using a lot of co signs or the law of sines. Right now we can't use either immediately, but we can easily find the third angle measure. And once we do we will have an angle measure and the length of its opposite side which allows us to use the law of sines. So let's find the measure of angle. See subtract from 1 80 the measure of angle A. And the measure of angle be that gives us a measure of 103 degrees for angle seat. Now we can use the law of sines because we have angle C. And the length of side see its opposite side. We can find side A. With the law of sines A. Over the sign of angle A. Yeah. Is equal to see over the sign. I mean we'll see multiply both sides. Okay, by the sign of 42 degrees. Yeah. And the calculator in degree mode will tell us that the length of side A. Is 0.82 Yeah. Mhm. We can find the length of side be the same way with the law of sines B. Over sign of angle be. Yeah. Is equal to see over the sign of angle. See. Yeah, multiply both sides by the sign of 35 degrees. Mhm. Yeah. And our calculator will tell us that the length of side B is 0.71 Yeah. And the triangle has been solved.

In this question, we are going to solve an oblique triangle using the given information. Now the given information includes two sides and the angle in between that tells us that we could use the Law of co signs. The other thing that we know is that we do not have the opposite side of the only known angle. So that means we cannot use the law of Science. So you have two different ways to decide which law we should use. And we have decided that we're going to use the law of co Science we would use in this case, C squared equals a squared plus B squared minus two times a times B times co sign of angle. See, let's find that missing side. Yeah, A squared plus B squared minus two times A times B times the co sign of angle. See, we can do a little bit of math before we pick up our calculators, 10 squared plus 12 squared 100 plus 144 is 244. Two times 10 times 12. 20 times 12 is 240. Yeah. Mhm. Yeah. Now I'm going to pick up my calculator and enter the square root of 240 for minus 240 co sign of 70 degrees. And I will find the length of side see is 12.7 to 5. Mhm. Yes. Mhm. Uh huh. Now that we do know an angle measure and its opposite side. We can switch to the law of sines and we can use the law of sines to find either the measure of angle A or the measure of angle be. It does not matter which one. I'm going to find the measure of angle a sign of a over side A. Which was given equals sign of angle see? Yeah. Which was given over side see which we found using the law of coastlines fix that for us. Okay. Okay. Alright. Multiply both sides by 10. Yeah. And then find the inverse sine. Yeah. Construction. Yeah. Yeah. Yeah. Yeah. It's a fine inverse sine of 10 signs 70 degrees divided by 12.7 to 5. And the measure of angle A is 47.6 degrees. Now we can find the measure of angle be to do so we would subtract from 1 80. The measure of angle C. Which was given. And the measure of angle A, which we found the measure of angle be is 60 to 4 degrees. And the triangle has been solved using the law of coastlines and the law of Science. Thank you.

Yeah. In this question, we are going to use the law of sines to solve an oblique triangle. The reason we're choosing the law of sines is because we've been given two angles and it's easy to find the third. So even though it doesn't look like we have the needed information which would be aside and its opposite angle. We can find that missing angle very easily By subtracting the first two from 180 An angle a has a measure of 161°.. Now we can use a lot of signs. Let's find side B. Side B over sign of angle be is equal to side A. Over sign of angle A Multiply by both sides by sign of 12°.. And in your calculator that's in degree mode, you will find that side B has a length of 102.18. We can also use the law of sines to find side see see over sign of Anglesey is equal to a over sign of angle A multiply both sides. Yeah, Inside C has a length of 59.89

We are given a quick 40 to dig these be equal study fire degrees anti equals 1.2. Here we can use C equals one a D minus. In my mystery To find the third angle, assemble three young girls off Rangel is 1 80 to see its 103 degrees. And now we use law off signed. So sign a upon a equals science See a bone See which means that a would be equal Don't see sign a a bone science e So we plug in the values and use a calculator which gives us the value off a and that is equal 2.8 to 4 similarly vilifying week. So we know that sign be upon the equal scientist a bouncy and be equal sees. And we upon sci fi you plug in the values again to find the value of B which is equal. Do 1.2 Scientist If I a born sign 103 the best 1030.71


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