Solve each triangle ABC that exists.

B = 72.2...

Question

Solve each triangle ABC that exists.

B = 72.2°, b = 78.3 m, c = 145 m

Accepted Answer

Hello, everyone. We are asked to find the missing side lengths and angles of the triangle. ABC, we are given angle B is 61.1 degrees. Side B is 99.8 m. Side C is 183 m. Our answer choices are A angle A is 48.6 degrees. Angle C is 70.3 degrees and side A is 156 m B. Angle A is 70.3 degrees angle C is 48.6 degrees and inside A is 156 m. See angle A is 48.6 degrees. Angle C is 70.3 degrees and side A is 131 m D no triangle exists. So I'm gonna use the law of signs recall that that's a ratio and that states that side A divided by the sine of angle A equals the side B divided by the sine of angle B equals the side C divided by the sine of angle C. So in this problem, what we are given are B's and C's. So that's the section of this ratio I'm going to start with. So I'm gonna substitute values in. So the side B is 99.8 m. So that'll be the top of my first fraction. It'll be divided by the sine of angle B. So the sine of 61.1 degrees, this will equal our sign or sorry, our side C so 183 divided by the sign of Anglesey, which is our unknown. So let's cross multiply and I get 183 multiplied by the sign of 61.1 degrees equals my other diagonal. So 99.8 multiplied by the sine of angle C get angle C by itself. I'm gonna start by dividing 99.8. So we have that the sign of angle C will equal 183 multiplied by the S of 61.1 degrees divided by 99.8. So I'm gonna place this in my calculator. Um First make sure your calculator is in degree mode. So that way you get a value and I get that the S of angle C is equal to 1.6053. Now, typically I would take the inverse sign here, but I'm noticing something. The sign of any angle like theta has to be less than or equal to one 6.053 is greater than one. So this means that no triangle exists because we cannot take the sign of that. We will not get an answer. So no triangle exists. This is answer choice D have a nice day.

Struggling with Trigonometry?

Solve each triangle ABC that exists.

B = 72.2°, b = 78.3 m, c = 145 m

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Law of Sines practice set

Struggling with Trigonometry?

Solve each triangle ABC that exists.B = 72.2°, b = 78.3 m, c = 145 m

Watch next

Law of Sines practice set

Solve each triangle ABC that exists.

B = 72.2°, b = 78.3 m, c = 145 m