Apply the law of sines to the following:

A ...

Question

Apply the law of sines to the following:

A = 104°, a = 26.8, b = 31.3.

What happens when we try to find the measure of angle B using a calculator?

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the measure of angle B in the chang ABC where angle A is 119 degrees side A is 37.2 units long and side B is 48.5 units long. For our answer choices A says that B is 26 degrees. B says it's 47 degrees C says it's 37 degrees and D says no triangle exists no. Oh And we can also use our calculator to help us solve. Now, in order to solve, in order to figure out the measure of angle B, let's try to sketch our triangle here. Let's assume that it exists. OK. In that case, then we'll have an angle A, an obtuse angle. OK. Obvious anger being equal to 119 degrees and four or triangle. Then if this is anger A, we could say this angle is anger B. Let me put that properly here. We could say up here is angle B and down here is C and based on how we name triangles, if angle A is here, then side A would be opposite to it. So the opposite side to A, our angle A is 37.2 units while the opposite side to B is 48.5 units. OK. So if our triangle exists, it would probably look something like this. So now if we're going to determine the measure of angle B, OK, we're determining the measure of angle B, then we have to think about the information we have. So what do we already know? Well, we know that we have the value of anger A and the value of the side opposite to it. We also know that we're trying to find the value of anger B. We don't know what it is, but we know the value of the side opposite to it. So we have a pair of angle and sides. How can that help us? What do we know about angles and sides in a triangle? We recall that we have the law of science and by the law of science, what it says is that the sine of an angle to its opposite side in a triangle is the same all throughout the triangle. In other words, by the law of signs, the sine of anger A to side A, the ratio of sine, the ratio of the sine of A to anger A is the same as the ratio of the sine of B to sine B, which is the same as the ratio as the sine of anger C to sine C. Now, in our problem here, we know the sign of A, OK. Or rather we know the value of anger A. We know the length of side A, we don't know the value of angle B but we know the length of side B. So we can use this idea here to help us to solve for the sine of B. Because now this tells us that the s of angle B to side B which is 48.5 units is going to be equal to the sine of angle air which is 119 degrees two side air which is 37.2 units to, to solve for B first, we can multiply both sides by 48.5. So that tells us that the sine of B equals 48.5 multiplied by the sine of 119 degrees divided by 37.2. And know if we were to work out this expression here, then 48.5 multiplied by the sine of 119 degrees divided by 37.2 would approximately be equal to 1.1403. OK. Uh 24 decimal places. Now there's a little problem that we have here. The sine of a value cannot be greater than one. The sine of a value exists between negative one and one. Those are its boundaries. So here, if it says that the sine of B equals 1.1403 that means there is no possible value for A B. In other words, this tells us that B does not have a solution. And if B does not have a solution, if there is no value for B, that means that the triangle cannot exist. Therefore, the correct answer would be answer choice. D no triangle exists for the measurements given for triangle ABC. Thanks a lot for watching everyone. I hope this video helped.

Apply the law of sines to the following:

A = 104°, a = 26.8, b = 31.3.

What happens when we try to find the measure of angle B using a calculator?

Key Concepts

Law of Sines

Ambiguous Case of the Law of Sines

Calculator Functions for Trigonometry

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