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[-/0.2 Points]DETAILSSPRECALC7 6.6.007_MY NOTESASK YOUR TEACHERPRACTICE ANOTHERUse the Law of Cosines to determine the indicated angle 0. (Assume answer to two deci...

Question

[-/0.2 Points]DETAILSSPRECALC7 6.6.007_MY NOTESASK YOUR TEACHERPRACTICE ANOTHERUse the Law of Cosines to determine the indicated angle 0. (Assume answer to two decimal places:)68.01, b = 36.38, and € = 42.85. Round yourNeed Help?Read lt Waich ltJalkto Iuter10. [-/0.2 Points]DETAILSSPRECALC7 6.6.008_MY NOTESASK YOUR TEACHERPRACTICE ANOTHERUse the Law of Cosines to determine the indicated angle 8. (Assume & 124.5, b = 60.1, and c = 159.5. Round your answer to the nearest degree.)Need Help?Ra

[-/0.2 Points] DETAILS SPRECALC7 6.6.007_ MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the Law of Cosines to determine the indicated angle 0. (Assume answer to two decimal places:) 68.01, b = 36.38, and € = 42.85. Round your Need Help? Read lt Waich lt Jalkto Iuter 10. [-/0.2 Points] DETAILS SPRECALC7 6.6.008_ MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the Law of Cosines to determine the indicated angle 8. (Assume & 124.5, b = 60.1, and c = 159.5. Round your answer to the nearest degree.) Need Help? Raudlt elkto Iuior



Answers

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

We are going to solve an oblique triangle using the law of co signs at least. That's what we'll start with. And that's because we've been given the three sides of the triangle when we have been given the three sides of the triangle, we want to solve for the largest angle first, which would be opposite the longest side. So let's find the measure of angle. See first using the law of co signs, I'm going to substitute in C squared equals a squared plus B squared minus two times a times b times co sign of angle. See And that's what we're solving for. Let's do some of the math. Eight square to 64. Next I want to do seven squared plus three squared to get 58 then two times seven times three. Yeah. Which is a coefficient of co sign of C. Subtract 64 minus 58. Yeah. To get six and divide both sides by negative 42. Okay, Finally take the inverse co sign of both sides. Mm. Yeah. Oh. And you'd get the measure of angle see to equal 98.21 degrees. Now that we know an angle and it's opposite side. We can use the law of sines to find our next missing angle. You can find angle or angle B. That is your choice. Let's find angle A. I would set up law of sines as sign of angle A over side A equal sign of angle see over side, see multiply both sides by seven and take the inverse sine 98.21. The inverse sine will tell us that the measure of angle A is 60 degrees. Yeah. It's finally, we can find the measure of the third angle by subtracting the first two from 1 80. Yeah. Mhm. And that tells us that the measure of angle B is 28.79 degrees. To do some double checking. You can always add up real quick the measure of all three angles, because certainly they should add to 1 80. In this case they do again as we are given three angles of an oblique triangle. You will use the law of co signs to find the largest angle first, and then the law of sines to find a second angle and third subtract the first two angles from 1 80 to get the measure of the third angle, and the triangle has been solved.

In this question, we are going to solve an oblique triangle using the law of co signs. Starting with the law of co signs. And that's because we've been given the length of two sides and the measure of the included angle side, angle side. Let's adapt the law of co signs to fit are given information. Okay? We've been given angle A. So I'm going to start my law of co signs with A squared equals B squared plus c squared minus two times B. Times C. Times co sign of angle A. Now we substitute in the values that we've been given, B squared plus C squared minus two times B times C. Times co sign of angle A. In fact, let me go ahead and take the square root in my next step, 15 squared 30 squared two times 15 times 30. And you can simplify some more if you'd like or you can put everything straight into your calculator as you see it. And you will find that the length of side A is 18.59 Now that we know an angle and it's opposite side. We can solve for one of the other missing angles by using the law of sines. If I wanted to find angle B, I would set up law of sines to say sign of angle be over side B equal sign of angle A. Yeah over side A. Multiply both sides by 15 and to find angle B. Take the inverse sine of both sides. Make sure you use parentheses properly. Okay? And you will get 23.79 degrees for the measure of angle be 23.79 Finally, we can find the third angle by subtracting the first two angles from 1 80. The measure of angle see is a result of 180 degrees minus the 30 degree angle that was given minus the 23.79 degree angle that we found. And the measure of angle see is going to be 100 and 26.21 degrees. And as a quick check, something is wrong. If you're three angles does not do not add up to 1 80 they should add up to 1 80 here. They do. So we solved for side angle side using the law of co signs, finding the measure of the side opposite the given angle first, the triangle has been solved.

In this question, we are going to solve an oblique triangle using the law of co signs. We're going to start with the law of co signs because we've been given to side lengths and the measure of the angle that is included, side angle side. We cannot use the law of sines because we only have one angle measure and we do not have its opposite side length. Yet we need to find that first. Using the law of co signs, lot of co signs we want to use would be c squared equals a squared plus B squared minus two times a times B times co sign of angle. See, let's let's substitute in the information we've been given to solve for side. See A squared plus B squared minus two times a times B times co sign of angle. See nine squared is 81. 4.5 squared is 20.25 two times nine times 4.5 is 81. Okay, I'm gonna do a little bit more math as I take the square root, 81 plus 20.25 is one oh one 0.25 minus 81. Co sign of one oh five. And I'm going to go ahead and type that in with my square root right now to find the length of side, see as 11.6 Now we do have an angle measure and its opposite side length. So we can use the law of sines to find either the measure of angle A. Or the measure of angle be, let's find the measure of angle B. With a lot of signs. Sign of angle A. Over side A. Is equal to the sign of angle see Yeah over side. See multiply both sides by nine and take the inverse sine. Make sure your calculators in degree mode and also put parentheses where they belong. And you will find that the measure of angle A is 51.85 degrees. Now we can find the third angle. You could use the law of sines again, if you wanted to, you could be crazy and use the law of co signs. It's going to be easiest to use the fact that three angles in a triangle add up to 1 80. So the measure of angle be will be 180 degrees minus the given 105 degrees minus the measure of angle A. That we just found and the measure of angle B is 23.15 degrees. We've solved the triangle. Now you do know that if those three angles do not add up to 1 80 we definitely did something wrong. The fact that they add up to 1 80 is a little bit reassuring. We have solved the side angle, side triangle, starting with the law of co signs, then using the law of sines and finally subtracting the two angle measures that we found from 1 80. The triangle has been solved.

Were given a triangle and rescues the law of co signs to solve this triangle. And round our answers to decimal places were given the side length of the triangle. A. B. And C. A. is equal to 1.42 B equals 7 5 and C equals 1.25 Just thinking mhm sixties. And we have to find the measure of ankles A BMC. So first I find the measure bangle A. Using the law of two signs we have the co sign of A is equal to B squared plus C squared minus A squared over two BC. Which is equal to 75 squared Plus 1.25 Squared -142 Squared All over two times point 75 Times 1.25. Mhm interesting. Mm 118 year old parents were texting you saying you're black? You're crazy. Mhm. Yeah. It's a cat man. Yeah. Yeah. She um yeah, I don't understand what you do. Mhm. This is about .05792. I. You have. And since this is positive, it follows that a measure of our angle A. Is approximately live The Inverse Co sign of .05792. Yeah. Which is about hi change 86.68°.. I'm sure as fast as they can ours will be to find the measure of angle B. I'll use the law of sines. We have the sign of angle B. Is equal to B. Times the sine of angle A. Over A. And so this is approximately points there 0.75 times this sign of 8668° over 1.42. Use also exactly anything. $3. That's how I had to walk around the mall attached to release help. Mm assaulted the woman who gives that samples and the people. Mhm. No way real partner leaves. But these so This is about 5- 7 3. Yeah. Mhm. Mhm. And therefore measure of angle B is approximately the inverse sine Of 5: 7 3. Yes. I it's just salt. This is the salt. Yes. Yeah. Me and my best friend too. Which is approximately think it's not your age is it's not the heat. It's the humidity. Mhm. It was like a child. Yeah that was that was a week 31.82°.. I'm a grown man. Yeah. And therefore measure of angle C. Is equal to 180 degrees minus measure of angle A minus B. Which is about 180° -86.68 -3182. And this is approximately 61 5°.. Mhm. That's salt. Yes, spoke me. It's a plate of sodium.


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