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Sin B2bc cos Asin C2ab cos Csin Asin B2) Complete the Iaw of cosines equation:c = 07 _ 622abcos Acos €cos BCcos ACCos B...

Question

Sin B2bc cos Asin C2ab cos Csin Asin B2) Complete the Iaw of cosines equation:c = 07 _ 622abcos Acos €cos BCcos ACCos B

sin B 2bc cos A sin C 2ab cos C sin A sin B 2) Complete the Iaw of cosines equation: c = 07 _ 62 2ab cos A cos € cos BC cos AC Cos B



Answers

For any triangle, derive the formula $$ a=b \cos C+c \cos B $$ [Hint: Use the fact that $\left.\sin A=\sin \left(180^{\circ}-B-C\right) .\right]$

100 Today we're going to start problem number 40 from the section No go. Thanks. Here The given that does and is given with this 65 degree and I will be given within 72 degree. I'm fight Michelle seven. But these things can direct personally, Renee. Rancor. Okay, and just be a president. So this can be which is 65. This can be logistical sanded group. You did. He said this will be side a bit. It'll beside B which Meshal's seven. This is science. See, this measures angry sea so must apply law Fight to find inside it that this sigh why you need to find, like five years but because saying beauty be fine is we can write 7 65 side is here Science 72 divided by Okay, you go seven. So I think that yeah equals 6.67 There angle see angle C equals 1 90 degree My list 65 plus 70 physicals. Larne 80. Why not select? If I Why not send it? It comes to be at our for day three activity. Then I'm play again. Loss. I find side. See blow that is sign see divided by C Because sign OK, divided by year. Fine. See? See, We know for day three Really by sea Because sighing 65 degrees divided by Here you is 6.67 from a good C equals 5.2 That's there. No for question. Thank you.

Were given two angles and a side and we're supposed to solve the triangle. Um, and the sense to stand please, just to find the missing candle and missing angle which is in Bill C, which is easier profiled interior angles of trying without under aged checklist. So if you subtract the other given angle, we then get angle C B C angle so 180 to land on 65 My not 7 to 2 use us seem to be 43 degrees. And from there we can find the missing sides. You can started a a We used them all sign So a divided by sine and he which is 65 decrease equals two be which is seven divided by sandy bees it into two degrees. So we make a the subject to the formula. Why cause more playing with planned city Fash they But I didnt site Oh, sign said into to decrease. And, uh but science 7 65 time seven divided by science and into two. It gives a 6.67 Greece and then we can find the final side, which is side see so see all yangzi regions for the three degrees in cost to A, which is a is, uh cannot use. B B is seven, divided by Sign B, which is answering to so see easy cost to seven signed 43 degrees divided by sign said into two, which is so sign their fortune three divider Dubai Sign 72 which is five point as they don't and then that's it.

Okay, so the first part of those question asks us to verify. Ah, falling your question. The equation is a C is equal to B Times Co sign of a plus eight times Coast Annabi. Now everything is labeled done here. B is equal to 78 miles or a side bees labeled 78 miles. Angle A's 25 degrees side A is 37 miles, and angle B is 117 degrees. And if we add these two terms together, you get that. They do, in fact, equal 53.9 by, uh, 53.9 miles. And this is in fact, I see now. I also asked us to use due to different forms of the law fco science, to show that this holds true for any triangle. So let's go. Let's try to make sure sees correct. Using another form, we use ah, following equation for the love coastlines. Another one and C squared equals a squared plus B squared minus two a b Times co sign of Anglesey. So let's go in and square root everything to isolate, see? And when we do this, we get that side sees again in fact, 53.9 miles. Now let's go ahead and use a loft coastlines to make sure that the angles remained the same since assets used to different forms of it. And we'll be making sure that Anglesey is that's pretty artsy. Anglesey remains true to the love coastlines. So Ah, we're gonna use the alternate form love coastlines, which is the following. It's gonna be coastline inverse of a squared plus B squared minus C squared over to a B. And when we do this, we do, in fact, get that C is equal to

So in the given question we have a right triangle abc, right? And we are given that A. B. Is equal to 24 centimeters. Bc is seven centimetres. And we are told to find sign A cause A. Because see and sign C. Right? So in general what we can do is if we have a triangle say we have a triangle peak you are. And there is an angle theta in the sand group, the sign of this angry theater. So this is a right angled triangle, right? And this is the Aiport news. So this is the all close inside. Faucet side to think to and this is the are just inside, right? So when we take the value of science theater, what we do is we take the ratio of the length of the opposite side divided by a high fitness. And when you take the cause of this angle costly to what we do is we take the artist inside the length of their descent side. They were in by the length of the high partners. So this is the method that we are going to use here. So before that we need to find the length of the high Putin's. Right? Which is a C. Over here. So you can use the pythagoras theorem, which says that in a triangle, in a right angled triangle, the square of the hypotenuse the square of the length of the high pony ins oh, is equal to the son of squares. Off squares. Are the are there two saints? The other two sides of the triangle? So here we have a B and B. C. Right? So a C squared is then equal to a B squared plus B C squared. Which is equal to 24 squared plus seven squared and 24 squared plus seven squared is equal to 625. From which we can write a serious equal to the square root of 16 6, 25 which is 25. So we have found the length of the high powered news as 25. So now it is easy to calculate age of this uh Econometric criminal metric ratios. Or we can say the sign of the Andrew A. Can be taken as the office. It scientist. The angle A. Is seven and the length of the high partners is 25. So sign A. Seven by 25. Similarly, when we take cause we'll take the charges inside to A. Which is 24 and divided by the high partners 25. Now when we take sign, see the artist in the opposite side. To sign the angle C. Is the side A. B. Right, So it is 24 which is the opposite side. They were led by high partners 25. And when we take because of the sand, will see they are just inside as D. C. So we will have seven. They were led by the high partners metres, which is 25 as the answer. So this is how we find the trigonometry ratios from a given right angled triangle. I hope you understood the method. Thank you.


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