Solve each triangle ABC.

B = 42.88°, C = 102....

Question

Solve each triangle ABC.

B = 42.88°, C = 102.40°, b = 3974 ft

Accepted Answer

Hello, today we are going to be finding the missing sings and angles of the triangle. ABC. We will also be labeling this information on the generic triangle. So we are told that the angle B is equal to 38.77 degrees. The angle C is equal to 109.45 degrees. And the side length B is equal to 4726 ft. So we are missing angle a side length A and side length C. How can we start finding this missing information? Well, we can start by solving for angle A. In order to solve for angle A, we will use the angle sum property for a triangle. The property states that the sum of all three angles within a triangle must equal 180 degrees. So if we take angle A and sum it with angle B which is 38.77 degrees and some that with angle C which is 109.45 degrees, this should equal to 180 degrees. So let's go ahead and solve for angle A 38.77 plus 109.45 will equal to 148.22. So we have a plus 148.22 is equal to 180 degrees. Subtracting 1 48.22 to both sides of this equation will give us an angle A is equal to 31.78 degrees. This is going to be the first piece of missing information that we need. And we will also label this angle on our triangle. So now that we have all three angles, how can we use these values to solve for the side links A and C? What we can do is we can use the law of science. The law of sign states that we have three equivalent ratios. We have the sine of angle A divided by the S length A is equal to sine of angle B divided by the S length B is equal to sine of angle C divided by the S length C. What we can do is we can take any two of the three ratios and set them equal to each other in order to solve for the missing side links. So let's go ahead and start by solving for the side length A. Now looking at the triangle, we have the angle and the side length for B and we have the angle for A but we are missing the side length A. What this means is that we can take the ratio with respect to B and set it equal to the ratio with respect to A. In order to solve for the side length A that will give us sine of A divided by little A is equal. The sign of B divided by little B. In order to solve for A, we will cross multiply both of the ratios that will leave us with a multiplied by S of B is equal to the SI length B multiplied by sine of A. We will divide both sides of this equation by sine of B. And that will give us the SI length A is equal to the S length B multiplied by sine of angle A divided by sine of angle B. We sold for angle A to be 31.78 degrees. We were given angle B as 38.77 degrees and we were given the side length B as 4726 ft. We can plug in these values and that will give us 4726 multiplied by S of 31.78 divided by s of 38.77. Now, at this point, I would recommend using a calculator to evaluate this quantity plugging in the quantity into a calculator will give us an approximate value of A to be 3975 ft. This is going to be the second measurement that we are looking for and we can label this on our triangle 3975. Finally, we need to solve for the value of C. Now we do have the angle C but we need the S length of C. So just like A, we are going to take the ratio with respect to B and set it equal to the ratio with respect to C in order to get the side length C. So we are going to solve for little C that will leave us with sine of B divided by the S length B is equal to sine of C divided by the side length C just like before we will cross multiply both of the ratios in order to solve for C that will leave us with C multiplied by sine of B is equal to the S length B multiplied by S of C. We will divide both sides of this equation by the sine of B. Leaving us with C is equal to the S length of B multiplied by sine of C divided by sine of B. Now we will plug in the values just like before we know that the side length B is equal to 4726 angle C was given to us as 109.45 degrees. So we will multiply this value by sign of 109.45 degrees and divide this value by sine of B which is s of 38 0.77 degrees. Just like before. We will use a calculator to evaluate this quantity. And this will leave us with C is equal to 7106 ft, which is going to be the final piece of information that we are missing. So just to recap, we use the sum angle property to solve for angle A which came out to be 31.78 degrees. We use the law of signs to solve for the sign length A which is 3975 ft. And we use the law of signs to solve for the side length C which is 7116 ft. With that being said, the answer to this problem is going to be a. 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.

B = 42.88°, C = 102.40°, b = 3974 ft

Key Concepts

Triangle Sum Theorem

Law of Sines

Finding Side Lengths

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