Use the law of sines to find the indicated part of each triang...

Question

Use the law of sines to find the indicated part of each triangle ABC.

Find b if a = 165 m, A = 100.2°, B = 25.0°

Accepted Answer

Hello, everyone. We are given a set of measurements that describe triangle ABC. We want to use the law of science to find side B. We are told the measure of side A is 394 m. Angle A is 108.8 degrees. Angle B is 43.1 degrees. Our answer choices are a 296 m. B 312 m C 284 m D 349 m. So if we're using the law of signs, recall that, that states we have ratios that are the side of A divided by the sine of angle A equals the length of side B divided by the sine of angle B equals the length of side C divided by the sine of angle C. Since in this problem, we only have A's and B's, we're going to use just that section of our ratio. So the side A has a measure of 394 divided by the sign of angle A. So the sign of 108.8 degrees, this is gonna equal our unknown, which is lowercase B, our side B divided by the sine of angle B. So the sine of 43.1 degrees to solve this, we are going to cross multiply. So I will have B multiplied by the s of 108.8 degrees. That will be equal to 394 multiplied by the sign of 43.1 degrees. Since I want to find B I'm gonna divide both sides by the sign of 108.8 degrees. So I know that the SI B will equal 394 multiplied by the sine of 43.1 degrees divided by the sine of 108.8 degrees. I'm gonna put this in my calculator. But first, I want to make sure my calculator is in degree mode or this will not work out. And when I place it in the calculator, I get 284.382 m though, we're not told where to round to all of our answer choices are rounded to the nearest whole number. So I'm gonna say our answer is that side B equals 284 m. And that's answer choice. C have a nice day.

Use the law of sines to find the indicated part of each triangle ABC.

Find b if a = 165 m, A = 100.2°, B = 25.0°

Key Concepts

Law of Sines

Angle Sum Property

Sine Function

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