Solve the triangle if a103a35b20a103a35b20 if no answer...

Solve the triangle if ∠A=103∘,a=35,b=20.∠A=103∘,a=35,b=20. If no answer exists, enter DNE for all answers. ∠B∠B is degrees ∠C∠C is degrees c=c= Assume ∠A∠A is opposite side aa, ∠B∠B is opposite side bb, and ∠C∠C is opposite side cc. Round all answers to 2 decimal places as necessary.

Transcript

00:01 Using the given information, we have to determine if 0, 1, or 2 triangles are possible, and then if any triangle is possible, we have to determine all the values for the triangle.

00:10 So looking at the given information, b equals 35, beta equals 25 degrees, and a equals 20 .5, nothing seems particularly off about it, so we can assume that only one triangle is possible.

00:24 So we'll first start off by finding alpha due to the fact that the information we're given, b, beta, we'll make it simplest to first find alpha using the law of signs and from there we can look at gamma and c so first i'll set up the equation for the law of signs so we get the sign of alpha equal over a equals the sign of beta over b we should first solve this for the sign of alpha so to do that we'll just multiply by a so we get the sign of alpha equals sine theta times a over b so we know the value is beta a and b so we'll just plug those into this equation and solve for the sign of alpha so we get the sign of 25 degrees times 20 .5 divided by b which is 35 when you solve for this you'll get that the sign of alpha is equal to approximately 0 .2 now we actually want the value of this angle and we can see here from the 0 .247 value that since this is within the range of the sign function, which is from negative 1 to 1, you can see here that this triangle is definitely possible.

02:02 So we can definitely solve for alpha where we'll just take the sign inverse of the number we just found 0 .247 and we'll get the alpha is equal to approximately 14 .5 degrees.

02:17 This information we can now find gamma and also see.

02:21 We'll start by finding gamma since and we can use the fact that a triangle's angles all add up to 180 degrees and we already have the value of two of those angles.

02:33 So using that information we can find gamma.

02:36 So first we can write that 180 degrees is going to equal to the sum of all the angles of this triangle.

02:42 So that will be alpha plus beta plus gamma.

02:48 Since we want to find and gamma will solve for gamma.

02:51 So gamma equals 180 minus alpha minus beta.

03:00 We know alpha and beta already so we can plug those values in.

03:04 So you get 180 minus 14 .5 degrees minus 25 or 30 minus 25 degrees.

03:22 So using a little bit of math you'll get that gamma equals 140 .5 degrees...