Problem

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

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Problem 2 Medium Difficulty

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

Answer

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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

and the students here. We've been given a triangle, so let's just draw a triangle for stuff all. And then we'll discuss what you have to do, actually. So this is our triangle? No, some some of their dimensions of this triangle are given to us at this point, is a This point is given be this point is given, see? And this Anglin is known to us which is 1 33 degree on 33 degree. So every night Acropolis tow, avoid confusion. So this is 1 30 Sorry. What am I doing here? 1 33 degree. Now, one more thing. Actually, two more think this system on decisions being this side is still this with him. And it is given that this scientists, I would be so this much information we have we have given we have been given and we have to solve the triangle. So as you can see that this side, this side and the angle made by these two sides has given to us. So we can say that we know the we lose off s s, they're deciding goal sides. And we know that if for any triangle we know the values off I wrangle side That is the angle corresponding to these two sides which concludes our S s so we can easily apply here because I knew so let's just apply cause and will and find out the remaining remaining where loser the given tangle. So while applying cause I'm Goldwater Louisville Festival apply for this, I'd be so this will be square is equal to B squared is equal to a square. Let's see square minus two a. C costs be date Course me. So let's just substitute values and find out the value off small we that is the third site so b squad will be as it is we have the calculated This is 50 that it actually is the decide alighted here just to our confusion is equal. Do 50 not 15 Wait, because is the small lays the length of the side which is composite toe angle So angle is this decide opposite This is this This will similarly see will be this a serial This multi 1,000,000,000 lent offside which is opposite to angle t So angle sees this This is capability penalty So let offside see will be 15 opposite. This is 15. So C is equal to 50. So we know the value of ages 12 01 44. It is quite anyone. 44 plus sees 15 to 600 to 25 actually minus two, multiplied by a mild privacy is 12 sees 15 multiplication of these two will. We wanted to know when a team of the blood work was 3 60 3 60 And we know the value, of course, because actually, we know the value of B beast wanted it. Really? The value, of course. 1 30 30 will degree will be minus 0.69 My No. 0.69 So we can easily compare the value of B squad from here. So these square will be 1 44 plus 2 25 December 3 69 and this will become my nest multiplied by minus. This will come plus 3 16 months. 90169 This will be a to 40 year point for do for tiered 0.4. If we just at these two, this will become with 617 Find food. When will take root off this for calculating the value of people we'll get the approximate value of villages you get 24.9 So this can be approximately that spent. If I So this is all really be Know what you have to calculate? We know all the sides of the triangle, which is a B and C No, you look great angles and will be. We know the value of angle B. We have to calculate angle a angle, see? So we have to again apply the co sign. Do so Let's just apply cause handle again. Most awful will consider angle a so far. Okay, angle able. Apply here cause and will again, which will be a square is required to be square. Let's see square. Why not do BC cost a minus two bc cost. So let's just substitute the values will know all the values except cost this angle. So, Amy, you know the value off a pistol sees 15 toe s 12. This everyone What if all 12 scott is one hurting for is equal. Toby vehicle returned The value of B, which is 25 25. Scott will be six quantify 6 25 plus C square receiving or the value of C, which is 15. So it's is quite ugly. 25 minus two BC cost. So these 25 c safety when will multiply these two, this will become 3 75 3 75 multiplied by two Will again become 7 50 sen 50 Cause I know finally. So what? We're Louis. It will take this thing to the other side. So will get 7 50 course day and we have been he will be left with on the right hand side. This plus this minus this because this will get to the other side of silicon minus. So this will come out at 6 25 plus 2 25 minus 1 40 for this will become 706 from this sugar devalue off course A. It is nothing worth 706 divided Way 7 50 If you can clear this fraction, we'll get this will come out of the door point 941 Now, when we will take this course in what's really off the 0.941 will get the approximate value off angle A which will be when did agree. So this is our measure of angle. Now we have to kill cleared the other angle which is unknown, which is and go to see so far Angle t will again apply cause handle. So from this we will get C square is equal to a square B squared minus Who will be course? See So let's again just substitute the value CV northerly off sees 15 so 15 scuttled with 25 is equal to be value finished well, toe square will be 1 44 plus BV calculated the value off B which is 25 searches called with 6 25 minus two A B A s 12 is 25. Multiplication will be It's much collection. Every 303 100 will be multiplied by two against us. It will become 600 600 course, See? So just I'll write it properly. No, again we'll take this time this 600 cost c Actually, this is 600 years. So just let me light write this properly so that you don't get confused. 600 course seeing I will take this thing to the other side. 600 course. See, this is equal to 1 44 plus 6 25 minutes to identify. This will come out as 5 44 Now, from this figure, the really off course See, which is 5 44 divided white. 600 Right? During the day when we'll divide this 15 44 to address 600 this will come out as the arrow point 906 and will take costing worse off vessel again. Get the value off angle to see. It will again come out of 25. It will come out of a 25 degree. So this is our measure of angles to see. So what are the values we calculated? You can create the value of angle. See, we calculated the value angle A and we calculated the side B. So actually, vehicles rooted all the remaining values off this triangle Triangle ABC. So this was our solution, guys. So hope they understood the video. And thanks for watching

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