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 C = 74.2°, c = 96.3 m, B = 39.5

Accepted Answer

Welcome back everyone in this problem. The given set of measurements describe triangle ABC where angle C is 68.1 degrees. Side C is 27.4 centimeters and angle B is 32.2 degrees. We want to use the large signs to find the length of side B for our answers. A says it's 19.8 centimeters. B 15.7 centimeters C 13.4 centimeters and D 20.2 centimeters. Now, if we're going to figure out the length of side B, let's try to do a quick sketch to understand what our triangle may look like. OK. So we have our triangle, OK. Let's call this our triangle ABC. OK. Where angle C is 68.1 degrees. Angle B is 32.2 degrees. OK. And side C, the side opposite to angle C is going to be 27.4 centimeters, which means then that the side opposite to Anger A is side A and the side opposite to Anger B is side B. Now we are trying to use the law of science to find the length of side B OK. And if we look at side B, what do we know? Well, we know that side B is opposite to an B. OK. And we know the value of an B, we also know that side C is opposite to an C where we know both Angus C and side C. So we have a pair of angles and sides. Do we know anything about triangles that relates a pair of a known pair of angles and sides? Well, like our question tells us it's the law of science because recall that by the law of science, what that law really tells us is that the ratio of the sine of an angle to its opposite side is the same through the triangle. In other words, the ratio of S A to the sine of anger A is going to be the same as the ratio of side B to the sine of angle B which is the ratio of the side C to the sine of angle C. OK? No, this is pretty helpful because we already know the value of side C and the value of angle C. So we can find that ratio. So we can use that idea to help us then figure out the length of side B because by isolating this part here by using this idea, OK. This tells us then that side B two, the sign of B which is 32.2 degrees is going to be equal to side C which is 27.4 centimeters to the sine of C which is 68.1 degrees. Now that we have an equation with one unknown, we can solve for B because if we multiply both sides of our triangle by the sine of 32.2 degrees, then B is going to be equal to 27.4 multiplied by the sine of 32.2 degrees divided by the sine of 68.1 degrees. Now that we have this expression for B, we can go ahead and put it into our calculator and solve. Now, when we put this expression into our calculator, you should find that you get B to be equal to 15.73640812 centimeters. But remember all of our answers were into the nearest 10th of a centimeter. So if we go to the 10th of a centimeter in our answer, our result, look at the digit beside it, it's less than five. So that tells us then that we can round B to 15.7 centimeters. Thus side B is 15.7 centimeters long to the nearest 10th of a centimeter. If we look back on our answer choices, B is the correct answer. Coincidentally, thanks for watching everyone. I hope this video helped.

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

Find b if C = 74.2°, c = 96.3 m, B = 39.5

Key Concepts

Law of Sines

Angle and Side Relationships

Trigonometric Functions

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