Problem

Solve the triangle, if possible. CAN'T COPY THE …

08:05

Problem 3 Medium Difficulty

Solve the triangle, if possible.
CAN'T COPY THE FIGURE

Answer

$A \approx 36.18^{\circ}, B \approx 43.53^{\circ}$ $C \approx 100.29^{\circ}$

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Precalculus

Algebra and Trigonometry

Chapter 8

Applications of Trigonometry

Section 2

The Law of Cosines

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Video Transcript

restaurants here we have been given a triangle, so let's just draw a triangle for stubble and then we'll decide what you have to do. So you did it ever tangle? Now some of the mission of the stranglers given to us. So this point is a point. A, this is B. This is see further. It is known that this scientist 14 this is what in this, Silas. Well, this is 20. Based on this information, we have to solve the remaining values off this strangle. So as you can see that we know that all the sights off this strangled So we actually know this as S s, which is referring to side side, side. So we know that when we know all the sides of the triangle weekend always used these sites. Values apply co sign rule and find out the angles so we can easily apply here. Course I lose. Right. So let's find out Masterful. Let's find off angle a. So for angle able to little apply questionable s squared is equal to be square plus c squad my next to bc, of course. Hey, no small. They will be small label be the measure off the side, which is opposite to angrily. So angle is this it? Opposite this angle? Decide the Sistol, so smallest well, similarly small B will be the opposite off and will be so This is 14 and sees similarly sees. 20. So let's just put the value most awful. A So a square is 12 days were living 44. This is equal Toby Square base 14 Toby's could have been 196 plus C square seems to indeed the squirrel before 100 minus to B. C. B's for 10 sees 20 so 20 multiply before 10 will be 22 80 multiplied by two will be 5 60 I have 60 costs cause is unknown to us now in the next step will take this minus 560 costs a will move to the other side So this will become 560 Cost A on the right hand side. We have here 1 96 plus 400 this 1 44 will also move to the other side. This will be comes up This will be subtracted. So all in all, we have the value off in this x plus 400 minus 1 40 But this will come out As for 50 toe no one will do at this fortitude with 560 will get the value. Of course. A this will come out as course is equal to this will come out a zero point 8071 It is 071 now from this difficult cleared the value off angle A. We'll take the inverse of this quantity 0.8071 So we will get his statistics 0.1 it the value off under level with 36.1 degree. This is automation off angle A No in the next step will calculate the value of angle. Be so for angle Beeville again apply cause I'm doing The square is equal toe a square. Let's see square minus two. Is he course the so Let's just substitute the values. Masterful piece Where so bees 14 b squad will be 1 96 This is a call to escort Rest well squad will be 1 44 plus C square sees 20 Squirtle before 100 minus two A. C is 12 ceased one day, so it will be to 40 multiplication of this will be to 40 to 40 million blood where two will be 40. So it will before dirty already cost me is unknown to us. So in the next time, what will You will take this quantity on the left hand side. And this to the right answer. So we'll get the belly for 30. Cost me. This will come outers. We will get you. Sorry, you'll get here. 400 plus 144. And this will get but get subtracted. So 400 plus one for two for minus 1 96 When will someone will do this? Calculation will get 3 40 years from 3 40 years. Sorry. From this negativity of Cosby, this is equal to two for $2. 40. This will be the point 725 properly. This was your concern to five. No, for final Devalue Fungal. We will have to take the cost in Warsaw, Visible turned to fight. When we take the inwards, we'll get the measure of angle B s 43 0.53 What? They 3.53 So this is the mayor of Bangle? Will be no. Last week, but not least we have to calculate the value of angle. See, So for calculating the value angle, see again, apply cause and will see Squared is equal to a squared plus B squared minus two A B course See from this will put the substitute the value off. See, baby. So CBS 20 so 20 square will be four under evil. Lewis Ace 12 is 14 So taste will 1 44 bees for 10 to 1 96 No year able to blabber to is 14 multiplied went well this will be 1 61 60 rule again Women the blood Where do this looking? Treat her taste. Six, 336 course. See, Because season one to us from this figure directly off course. See Saudi? No, because it is actually treated This six Kasey 3 36 course said this This quantity will move to the other side and this 400 will for the other side. This will become 144 plus 196 months. 400 This will become minus 60. From this, it would divide this money 60 with 3 36 will get the value cost C which will come out as minus off 0.1785 for finding out the value of myself angle. See, you will have to take this costing more from this country. So since this is a negative, we are sure that it will be the value of angles. He will be more than 90 degree. So when we eventually take this in worse causing worse off this quantity will get handled. CS 100 point tonight, 9.29 degrees. So this is our measure of Anglesey. So what? All the quantity zero calculator in here will kill a measure of angle, see 1,000,000 off angle B and measure off angle A also. And the site lent us that we have already known in the question. So all the all the remaining all the remaining wages of angle off this triangle is known to us. So this was our solution. Hope you understood the video. And thanks for watching

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