In Exercises 9–16, solve each triangle. Round lengths to the near...

Question

In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.A = 85°, B = 35°, c = 30

Accepted Answer

Hey, everyone in this problem, we're asked to find the missing side lengths and angle of the triangle. ABC. We're told that angle A is 95 degrees. Angle B is 50 degrees and side length C is 20. We're asked to express the links to one decimal place in the angle to the nearest degree. We're given four answer choices A through D each containing different values for the three things. We need to find side length A side link B and angle C. So let me write those three things that we're looking for at the top. We're looking for side A, we're looking for side B and we're looking for angle. See, and let's start with the angle. OK. We're already given two angles. We know that the sum of the angles in a triangle adds up to 180 degrees. And so right off the bat, we're gonna be able to calculate that side length. OK. So again, recall that angle A plus angle B plus angle C is gonna be equal to 180 degrees because it's a triangle substituting in our values angle A is 95 degrees plus angle B 50 degrees plus angle C is gonna be 180 degrees. Simplifying on the left-hand side, 95 degrees plus 50 degrees gives us 145 degrees. We're gonna subtract that from both sides to isolate for angle seat. When we get that angle C is equal to 35 degrees. So we've already got one of those missing values. We've found that missing angle angle C and we found it to be degrees. Looking at our answer choices, the only one that has angle C being 35 degrees is option D. So we expect that option D is gonna be the correct answer. We wanna finish out this problem. We would just wanna double check that we didn't make any mistakes calculating this angle. And it's good practice to know how to find these sidelines. OK? All right. So now we have side linky and Anglesey. OK. So we have the sideline in the corresponding angle. So let's think about using the law of signs to find our missing sidelines. Yeah, we're called the law of science tells us that the ratio of a particular side to the corresponding sign of the angle is equal for whichever side we choose right. So what we're gonna do is we're gonna start with side A, we wanna find side A. So the first ratio we're gonna look at is side A divided by sign of that corresponding angle. So angle A and we're gonna set this equal to the rate a ratio that we know. Now we know side link C and we know angle C. So let's relate it to C. So this is gonna be equal to C divided by sine of the angle C substituting in what we know we have a, a divided by sine of degrees is equal to divided by sine of 35 degrees. We're gonna multiply both sides by sine of 95 degrees to isolate for A, we get that A is equal to 20 multiplied by sine of 95 degrees divided by sine of 35 degrees. And if we work this out on our calculator, we get that A is approximately equal to 34. units. All right. So we have a rounding to the nearest decimal place. We're gonna get 34.7 units. OK? Which matches with that option D answer choice that we're expecting. OK. So that's good. So far, let's go ahead and do the same for side length B and we're gonna take the law of signs again relating B and C. OK. So we have B divided by sine of the angle B is equal to C divided by a sign of the angle C. Now, at this point, we could have related B to A because we just calculated side length A, we already know the angle A. So we could relate B to A you have to be a little bit careful. If you do that, you subject to some round off error in our answer for a and also if you made a mistake in your calculation for a, that mistake is gonna carry over into your calculation of B OK. So sometimes it's a good idea to try to stick with the values that you were given in the problem if you can. OK? So that's why we're using C. But again, you could use a all right. So side length B is what we're looking for. We divide that by sign of the angle B, 50 degrees. This is equal to 20 divided by five of 35 degrees, multiplying both sides by sign of 50 degrees. B is gonna be equal to 20 multiplied by sin of degrees divided by sign of 35 degrees. And we can write this as B is approximately equal to 26.7 units. So we found the missing angle angle C to be 35 degrees. Side length A is approximately 34.7 units. And side length B is approximately 26.7 units which corresponds with answer choice. D. Thanks everyone for watching. I hope this video helped see you in the next one.

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In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.A = 85°, B = 35°, c = 30

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