Determine the number of triangles ABC possible with the given ...

Question

Determine the number of triangles ABC possible with the given parts.

c = 50, b = 61, C = 58°

Accepted Answer

Hello, everyone. We are asked to find the number of possible triangles. With the following measurements. We have a side C that measures 70 A side B that measures 83 and an angle C that measures 79 degrees. Our answer choices are A one B, two C, none. So we're gonna use the law of science and recall that love of science says that we have a divided by the sine of angle A well equal to the side B divided by the sine of the angle B and the side C is divided by the sine of angle C. So we have a ratio. In this case, we are given B's and C's. So that's what I'm gonna set this up with. So side B has a measure of 83 divided by the sign of angle B which is our unknown at the moment. And that's going to equal the length of side C which is 70 divided by the sine of Anglesey. So we'll have the sine of 79 degrees. I'm gonna cross multiply. So I have 70 multiplied by the sine of B equals 83 multiplied by the s of 79 degrees to get the sine of B by itself. I'm gonna divide both sides by 70. So I have the sine of B equals 83 multiplied by the sine of 79 degrees divided by 70. I'm now going to use a calculator and put that whole fraction into it. Make sure that you are in degree mode when you use your calculator. And I get that the sign of angle B has to be equal to 1.6. I'm sorry, 1.16. Now, from here, I want to find what is B but I'm noticing something first sign cannot be greater than one. So the sign of any angle, so we'll call it theta has to be less than, or equal to one. So in this case, this is greater than one. So we actually have no triangle here, which means this is answer choice C none have a nice day.

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Determine the number of triangles ABC possible with the given parts.

c = 50, b = 61, C = 58°