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In Exercise !, solve the triangle shown In the figure Round lengths t0 3 rodecimal = places and uxpress angles t0 the nedrest tenth %f a degrec (SAow( ALL Wo30.4,50...

Question

In Exercise !, solve the triangle shown In the figure Round lengths t0 3 rodecimal = places and uxpress angles t0 the nedrest tenth %f a degrec (SAow( ALL Wo30.4,50,2

In Exercise !, solve the triangle shown In the figure Round lengths t0 3 rodecimal = places and uxpress angles t0 the nedrest tenth %f a degrec (SAow( ALL Wo 30.4, 50,2



Answers

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. $$a=30.4, c=50.2$$

All right, We're going to solve friend or giving those two dimensions A and C So a use they're burning for and C is a costume. See 0.2. Right. So to solve the triangle just a sketch just so much You can have a picture. Of what? Your dream. So this is an identical plan, but this is a be you see? No. What are you giving side A, which is inside that 0.4 saved sieges there. What a nice we choose. You have to do so on one side, B. Yes. So to get side B, you can use by the glory of yours. So the Pythagorean theorem instance that he's wind must be smooth is equal to six weeks. So the summer off the short of the squares of the other side is equal today square off the Lygia site. So since we want to get b squared, we have to take a to the other side gums and they get to this is equal to Well C squared is 50 point to threat. A squared is there between four square And then from there you can just see find square on set 50.2 spent minus the explain for I want to wait with the absolute finest. That's where we want to mambo. Now let's put it up in the car plate. I've been simply practiced in ancient cultures. Just put it slips. And you can make use of my kids to make sure that, you know, inputting. Correct. Then what do you get? There is 39 point nine flecks. Okay, so two to this small place to assume. So there's I units found in from then can Rick Umps. One angle that is missing so can use one in one of the issues Time, close and sign. Because now we got everything given will reside to use what we have. What is there? So we give you a sign for a while? Is that Julie? Always day. Because in case I made it in my big coalition himself, each something. So sign a is equal to oppose it over Justin. And the opposite is do you witness the 0.4 reminded why on it? Okay, let me just correct here. It wasn't over. I'm putting us composed over just in this town. So, Dante, when four demanded by 50 when two I didn't find excellent port sites. Sign off, saying a question signed explained for 2.2. Well, this isn't about girls and left. It is forced to antes have important tools to sit in the crease, and it's approximately. Round it off. It's 37.3, please. Now, to get beef, we use the scent that the two angles complimentary. It means that A and B adopt united, please. So if I know one off them, it's that the seven point the press absent for 90 get the angle and once I get stripped, too, went seven decrease true.

I felt sick. You look at solving this triangle with love. Co signs in this case were given vibius five sites, See is three in angle, 802 degrees. So start this question off. Let's just do a quick little sketch here of the information we have. So we start with Anglais. Ah, 102. So it's gonna be bigger than 90. We've got up to angle here, So let's say it's something like, Well, not quite like that. Let's say I don't know this. All right, so this is 102. Okay, we've got side B. Let's put side being here. Five in this side here is three. So this is angle a and then if I just kind of continue here. All right, this will be side. Hey, over here. If this is side, see, this is angle, See? And this is angle. Be here. So this is kind of what our triangle might look like. All right, So we can see based on this information, we've got two signs of contained angle between them were set up to find side eight first. So let's do that. A squared equals B squared, plus C squared minus two bc co sign of English Only when I know five squared plus three squared when it's two times five times three and then the co sign of 102. Okay, so 25 for five squared plus nine for three squared and then two times five is gonna be 10 times three is 30 And that 30 times co sign of 102. So, punching all this in our calculate, we get a square is gonna be able to 40 0.237 and then a few decimals, Which means that a if I square root, this value is gonna be six point 34 or rounding we get a is equal to 6.3. Okay, so now we have said A at 6.3. So we're good here. We've got three side length, which means with law co signs, I confined the value of either these two angles. Let's find angle. See, you could just as easily find the value of Angle B. All right, you're just formula would look a little different. So we're gonna have coast on C equals a squared plus B squared minus C squared all divided by two a. B So plugging in my values here, eh? We just found 6.3 and that's all squared plus R squared minus three squared And that's all divided by two times 6.3 for a times, five for beef. So simplifying the top here a little bit. I get 39.69 plus 25 minus nine, all divided by 63. So if I punch a lot of my calculator, I get co sign of C is equal to zero point eight 839 and a few decibels after that. Which means if I want to find the angle the angle of C, I need to inverse coast on that value. Okay, and you will get angle. C is equal to 27 0.875 or rounding. We get English Musical to 27.9 degrees. Okay, so almost done. All we need now is angle B, so we know all the angles should add up to 1 80 I could just do 180 miles the two angles that I know, all right, angle see, and the 102 degrees for a that was given in. You'll get angle B is equal to 50 0.1 degrees, and there's your triangle salt

According to given questions, we have be easy for two. Life seems equal. Do three on angle is equal to one. Did a little digging. Now, using lost four sign you can solve the other perimeters. So there were light using law off. Well, saying so That means Harry Light, first of all, squared is equal to b squared plus c squared minus to B C Costea. So five squared plus three squared minus two were deployed with five my deployed with please cost one little to David. So this is 25 plus nine minus cardi cause one little David. So he s squared is equal to 40 point four. So is equal to route 40 points. Four. So this is a cool into six point c. So now you can find out the perimeters with the help off law. Fine. So we'll light using law off ST we cannot it Science sees equal. Do see Sign A Divided by a. So this is three signed One little dignity, divided by 40.24 So this is equivalent to zero point for six six. So that means we can night angle. Sesay called sign in waas off 0.4626 That means angle seriously cool and 28 degrees. Now we can find any beers and will be easy for doing every degree minus C minus t so 1 80 degree minus doing the eight minus 102 So this is a 15 minute. So these are the values off angle B and C and a.


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