Without using the law of sines, explain why no triangle ABC...

Without using the law of sines, explain why no triangle ABC can exist that satisfies A = 102° 39', a = 15.9 ft, b = 21.7 ft. Choose the correct answer below. A. Because A is acute, it is the largest angle. Thus side a should be the smallest side, but it is not. Therefore, no such triangle exists. B. Because A is obtuse, it is the largest angle. Thus side a should be the smallest side, but it is not. Therefore, no such triangle exists. C. Because A is obtuse, it is the largest angle. Thus side a should be the longest side, but it is not. Therefore, no such triangle exists. D. Because A is acute, it is the largest angle. Thus side a should be the longest side, but it is not. Therefore, no such triangle exists.

Transcript

00:01 Use law of signs and explain why no triangle abc is possible that satisfies the given condition.

00:05 So let's use law of science first of law of science.

00:11 So in law of science we can use a over sign a because a and angle a both are known and the rest we can use the pair b over sign b because angle b is not known to us.

00:22 In other words we are trying to find angle b using law of science.

00:25 That's going to be a over sine a equal to b over sign b.

00:32 If you cross multiply then the value of sine b is going to be b sine a over a.

00:39 So that's going to be b is 21 .7.

00:43 Sign of angle a is 102 degrees, 39 minutes over side a where side a is 15 .9.

00:53 I'm not sure if you have an option to plug in minutes as well.

00:56 But if you don't, then it's totally fine.

00:59 You can convert this minutes to degrees by dividing by 60.

01:03 And adding to 102 degrees and over 15 .9.

01:08 So let's try to find the value of this expression, which is nothing but sign of b.

01:15 So let me just grab my calculator.

01:18 That is 39 over 60 plus 102, sign of this value times 21 .7 over 15 .9.

01:30 So this is coming as 1 .33.

01:32 Now the question is, does this even possible? because the range of sine theta is always between minus one to one.

01:42 So if this equation says that sign of an angle is 1 .33, this is not possible.

01:50 Because this is outside the range of sign, the maximum can be 1.

01:53 It can never be 1 .33.

01:55 It implies that there is no solution for angle b and hence no such triangle.

02:05 If we look at the options, it says that because a is acute is the largest angle, the side a should be the smallest or not, there's no such triangle...

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