Solve each triangle ABC.

C = 79° 18', c = 39....

Question

Solve each triangle ABC.

C = 79° 18', c = 39.81 mm, A = 32° 57'

Accepted Answer

Hello. Today we are going to be finding the missing pieces of information to the triangle. ABC. We are told that angle C is equal to 69 degrees with 28 minutes. We are told that side length C is equal to 31.92 millimeters and the angle A is equal to 36 degrees with 49 minutes. Let's go ahead and label this information on a generic triangle. So we have the side links A B and C with the respective angles of angle A angle B and angle C. Now we are told that angle C is 69 degrees with 28 minutes. We are also told that the side length C is equal to 31.92 millimeters. And we are told that angle A is equal to 36 degrees with 49 minutes. So what we need to do is we need to solve for the angle B and the sinks A and B. Let's go ahead and start by solving for the angle B, we can solve for the angle B by using the, the sum property for the angles of a triangle, the sum property states that the sum of all three angles within a triangle must add to 180 degrees. So if we take the sum of all three angles, which can be written as 36 degrees with 49 minutes plus 69 degrees with 28 minutes plus the angle B, this should equal to 180 degrees. We are going to use this equation to solve for angle B no, 36 degrees with 49 minutes plus 69 degrees with 28 minutes will give us a sum of 101 degrees with 17 minutes. So we have 101 degrees with 70 minutes plus the angle B is equal to 180 degrees. We will subtract 101 degrees with 70 minutes to both sides of the equation. And then that will give us the angle B of 78 degrees with 43 minutes. This is going to be the first piece of missing information that we need. And we will also label this value on our triangle. Now, how can we solve for the side links A and the side links B. In order to solve for these side links, we're going to use the law of signs. Now, the law of science tells us that we have three equivalent ratios. We have sign of angle A divided by si length A is equal to sine of angle B divided by S length B is equal to sine of angle C divided by S length C. What we are going to do is we are going to pick any two of the three ratios, set them equal to each other. And use that to solve for the side links A and the side links B. Now recall that the problem gives us the angle of C and the side length C. So we have all the information we need for the ratio with respect to C. We have the angles for B and the angle for A. But we are missing the side links B and the side links A. Let's go ahead and start by solving for the side length of A. In order to do this, we're going to take the ratio with respect to C and set it equal to the ratio with respect to A. So we have sign of angle A divided by the side length A is equal to sine of angle C divided by the side length C. We will go ahead and solve for the side length A by cross multiplying the ratios that will leave us with side length A multiplied by s of angle C equal to the side length C multiplied by sine of angle A. We will continue to suffer for A by dividing both sides of the equation by sine of angle C. That will leave us with side length A is equal to the side length C multiplied by sine of angle A divided by sine of angle C recall that the S length of C is 31.92 millimeters. The angle of C is 69 degrees of 28 minutes and the angle of A is 36 degrees with 49 minutes. If we plug in these values, we will have 31.92 multiplied by sine of 36 degrees with 49 minutes divided by sign of 69 degrees with 28 minutes. At this point, I would recommend plugging in this value into a calculator to help you find the value of the sign length A. After doing so, we should end up with a length of 20.43 millimeters. This is going to be the second piece of missing information that we need for the triangle. Now, we will repeat this process to solve for the side length B. Now we're going to use this ratio with respect to C and set it equal to the ratio with respect to B in order to solve for the side length B. So we will have sign of angle B divided by the S length B equal to sine of angle C divided by the S length C just like before we're going to cross multiply. In order to solve for the side length B, this will give us the side length B multiplied by S of angle C equal to the side length of C multiplied by sine of angle B. If we divide the sine of C to both sides of the equation, we will have the S length of B is equal to side length. C multiplied by sine of B divided by sine of angle C. And if we plug in the known values for the values of C and the angle B, we will end up with 31.92 multiplied by sine of 78 degrees with 43 minutes divided by s of 69 degrees with 28 minutes. After plugging this value into a calculator, we will end up with the S length B equal to 32.77 millimeters. This is going to be the final piece of missing information that we need for the triangle. So just to recap, we use this, we use the some angle property to solve for the angle B which came out to be 78 degrees with 43 minutes. We then use the law of signs to solve for the side length of A which is 20.43 millimeters and the side length of B which is 32.77 millimeters. With that being said, the answer to this problem is going to be B So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Solve each triangle ABC.

C = 79° 18', c = 39.81 mm, A = 32° 57'

Key Concepts

Triangle Angle Sum Property

Law of Sines

Angle and Side Notation in Triangles

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