Solve each triangle ABC that exists.

B = 39....

Question

Solve each triangle ABC that exists.

B = 39.68°, a = 29.81 m, b = 23.76 m

Accepted Answer

Hello, everyone. We are asked to find missing side lengths and angles of triangle ABC we are told angle B is 57.43 degrees. Side A is 65.29 centimeters. Side B is 79.86 centimeters. Our answer choices are A angle A is 43.55 degrees. Angle C is 79.02 degrees. And side C is 93.03 centimeters. B angle A is 79.02 degrees. Angle C is 43.55 degrees and side C is 93.03 centimeters. C angle A is 33.55 degrees. Angle C is 89.02 degrees. Side C is 93.03 centimeters D no triangle exists. So we're gonna use the law of signs to solve this recall. The law of signs is a ratio where we have the side A divided by the sine of angle A equals the side B divided by the sine of angle B is equal to the side C divided by the sine of angle C looking at what we're provided we have A's and B's. So that's the section of this ratio. I'm gonna start out using, I'm gonna fill in or substitute what I know. So the side A is 65.29 centimeters. We're going to divide that by the sine of angle A which we don't know. So I'm going to leave that as my unknown sign of angle A that'll equal the side B. So 79.86 divided by the sign of angle B. So this is the sign of 57.43 degrees from here. I'm gonna cross multiply. So I have 79.86 multiplied by the sine of A equals 65.29 multiplied by the s of 57.43 degrees to get the sine of A by itself. I'm gonna divide both sides by 79.86. So we will find that the sine of angle A equals 65.29 multiplied by the sign of 57.43 degrees divided by 79.86. I'm going to place this all in my calculator and see what we get. Um Recall that you need to make sure your calculator is in degree mode first. And I get that the sine of A equals 0.68. I'm gonna round it to nine. So now using the inverse sign, I'm going to take the inverse sign of 0.689 that will equal my angle A and we will get the angle A is 43.55 degrees. That's my first angle. Now to find my second angle, I recall that all the angles in a triangle total to 180 degrees. So here, if I want to find the angle C I can take 180 degrees, subtract the measure of angle A and subtract the measure of angle B. So we have 180 degrees minus 43.55 degrees for angle A minus 57.43 degrees for angle B. And that will give us that the angle at sea is equal to 79.02 degrees. All right, our two angles are done, we now have a side still defined. So to find the side, C, I'm gonna use another section of my law of science. So to find the side C, I'm gonna use that B divided by the sine of angle B will the side C divided by the sine of angle C. So substituting in those values 79.86 divided by the s of 57.43 degrees will equal lowercase C divided by the sine of 79.02 degrees. Again, I'm gonna cross multiply I have C multiplied by the sign of 57.43 degrees and that will equal my other diagonal. So 79.86 multiplied by the sign of 79.02 degrees to get the sea by itself. I'm gonna divide both sides by the sine of 57.43 degrees. So C will equal 79.86 multiplied by the s of 79.02 degrees divided by the sign of 57.43 degrees. And I will definitely be using a calculator to find that one out. And when I do, I get 93.03 when I round and our label is centimeters. So the side at sea is 93.03 centimeters. Now, checking my answer choices for a to be 43.55 degrees C to be 79.02 degrees and side C to be 93.03 centimeters. And that's answer choice. A have a nice day.

Solve each triangle ABC that exists.

B = 39.68°, a = 29.81 m, b = 23.76 m

Key Concepts

Law of Sines

Triangle Sum Theorem

Ambiguous Case of SSA

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