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Let the angles decimal place )tNangle beB, Y, wlth opporite SidesIengthrespectively. Use the LawCosinesfInd the remalningand anethe other angles (Rounoanswer1158;1...

Question

Let the angles decimal place )tNangle beB, Y, wlth opporite SidesIengthrespectively. Use the LawCosinesfInd the remalningand anethe other angles (Rounoanswer1158;12; b = 17

Let the angles decimal place ) tNangle be B, Y, wlth opporite Sides Iength respectively. Use the Law Cosines fInd the remalning and ane the other angles (Rouno answer 1158; 12; b = 17



Answers

Solve $\triangle A B C$ by using the given measurements. Roundmeasures of sides to the nearest tenth and measures of angles to the nearest degree.
$a=14, b=13$

So for this problem we are asked to solve the triangle by using the law of co signs and because I have angle C. And A. And B. I'm gonna use this law of coastlines formula. Over here we're both in my caesar on the outside. So I'm gonna go ahead and plug an avian see. Yeah. Yeah. Mhm. Mhm. Mhm. Mhm. Mhm. Yeah mm. And this problem is kind of nice because I can type this whole thing on the right into my calculator. But you want to make sure that you're in degree most since you're working with degrees. And that gives me C. Squared equals one oh 7.23. And then I'm gonna take the square root of that number to get see Which is 10.36. You decide now from here since I have a pair I can go ahead and use the law of sines to solve her Air B. So I'm gonna use C. And I'll just solve for a first mhm. Mhm. Mhm. Mhm. I'm gonna cross multiply. Mhm. Simple. And by both sides by 10.36. Yeah and since I'm solving for an angle I have to take the inverse of sign to get angle A. So I'm gonna take this in my calculator and the T. 84 that's gonna second sign them with a fraction in. Yeah And that gives me 35.52°. Mhm. So two sulphur be I'm going to add these two angles together And to attract them from 180 to get Angle B. Which is 85.18°. Yeah, Okay.

Well, everyone, this is Ricky and terrible from 31. And so this is a lot of science question where were given ankle unknown side, another angle with inside. So let's just write this out. Sign of 30 degrees over eight is equal to inside for five greens over a use cross multiplying. Get a equals 8 to 7 45 over. Son 30 and we simplify this. We get that a is equal to about so this video is helpful.

So now we have a triangle and were given some pieces of information on Let me just start toe label. So let's say that this is our triangle. I will label it Triangle A, B, C and little A would go here. Little bee will go here and little So you will go here. And we know that the measure bangle a is 110 degrees were given that side A is 28 and we're given that side B is 15. Now we know that this cannot be the case where we have more than one triangle. We can see that we have long side, short side angle, long side, short side angle. And we know short sidelong side angle is a possibility where there might be non and there might be one, and that mother might be too. But when we have this setting, it's going to be a unique triangle. So we're ready to set up love signs. And since the first thing will be finding is this angle be because we know we have ah, side angle pair here and we have a side and we confined that angle with love signs and I'm gonna put the angles on top. So the sign of Capital B is to side B, as the sign of 110 degrees is to its side opposite, which is 28. And we would be multiplying both sides by 15. And now we will have what the sine of the angle is and the sign of angle be Now, do make sure your calculators in degree Modi check that right before Andi. I've got it in degree mode. Be ashamed to do the problem right without but have mode, Rog. So we have 15 times a sign of 110 degrees, and then we're going to divide that by 28. Now. If this came out to be a value that was bigger than one, then we would know that this is an impossible setting. Sometimes we have triangles that actually we can't find. So there we go, and now we will need to use our inverse sine function to find angle beat. So I think of the inverse functions as Angle Finder's. And so the inverse sign. Let me find the button. Denver sign of a my second answer, and I have that. That ankle comes out to be angle B comes out to be 30 point two, and then it would round off to two places. Two or three. There's a to five. I'll also now we'll go back and really will find. Since we know now this angle, you know that this one is 30 0.23 degrees. It's gonna be very easy for us to find angle, see an angle. See, we're going to take 180 degrees minus these two. So and I'm gonna put, uh Well, I'll I was going to store that angle, but I won't need thio. So 180 degrees, minus 31 10 minus that answer. And I get my 39.77 degrees. So 39.77 degrees. So we have two of the pieces of information we know this ankle now and now last thing we have to do is find this side, see, and we're gonna have to again use law of signs. You can't use Pythagorean theory. Um, we don't have a right triangle. So now that we're looking for see, I'm gonna put see on top, see, is to the sign of its angle opposite. And that is 39.77 degrees it has. And now I'm gonna use this original pair that I was given 28 is to the sign of 110 degrees. And again, I'm gonna multiply both sides by the sign of 39.77 degrees. So we will have 28 times thesis ein of that ankle, which I already have in my calculator. So I could just do second answer divided by the sine of 110 degrees. And we get 19.6 Percy. And there we go. Those there are three pieces of information we were looking for are solved.

We have even is equal to seven. B is equal to agency is equivocal. 13 V use course General Correct. Remind the value of angle a angle. Be anger and angle. See cause I know Pangle Evil people Toby Square Policy Square Minuses. Quality buried by toe BC This is equal toe 80 square plus 13 X squared minus seven is part divided by two multiplied by eight multiplied by 13. If we simplify it, we get co sign off angle is equal to 0.388 from your angle. A physical because inwards off 0.88 we get angle is equal to 27.8 degrees after a simplification. Now what? Sign off angle B will be equally toe. 70 square plus 13 x squared minus eight is squared, divided by two multiplied by seven multiplied by parting. Now if we simplify it vigour. This is a world toe 0.846 From here, angle B is equal to cosign over soap. 0.846 we get angle B is equal toe, 32 went toe degrees. Now sign off Angle C is equal toe 70 square plus 80 square minus 13 is quite divided by two multiplied by seven multiplied by eight. When we simplify it, we get this is equal to minus 0.5 now angle civil because, of course, in worse off minus 0.5, we get angle. C is equal to 120 degrees. This is the value of Bengal sea.


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