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Solve triangle ABC if ZA = a = 40.2" b = 8.6 mi, and c = 17.1 mi.Using the Law of CosinesYour answer should accurate t0 4 decimal placesThus,mi_Your answer sho...

Question

Solve triangle ABC if ZA = a = 40.2" b = 8.6 mi, and c = 17.1 mi.Using the Law of CosinesYour answer should accurate t0 4 decimal placesThus,mi_Your answer should accurate t0 2 decimal placesUsing the Law of Cosines again, cosZB cos 8 Your answer should accurate t0 5 decimal places.Thus, B Your answer should accurate [0 2 decimal placesFinally; using the sum of angles for triangles, ZC = Your answer should accurate t0 2 decimal places. Assume Za is opposite side a , Z 8 is opposite side b,

Solve triangle ABC if ZA = a = 40.2" b = 8.6 mi, and c = 17.1 mi. Using the Law of Cosines Your answer should accurate t0 4 decimal places Thus, mi_ Your answer should accurate t0 2 decimal places Using the Law of Cosines again, cosZB cos 8 Your answer should accurate t0 5 decimal places. Thus, B Your answer should accurate [0 2 decimal places Finally; using the sum of angles for triangles, ZC = Your answer should accurate t0 2 decimal places. Assume Za is opposite side a , Z 8 is opposite side b, and Zy is opposite side € Submit Question



Answers

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$C=101^{\circ}, \quad a=\frac{3}{8}, \quad b=\frac{3}{4}$$

In this question, we have to use the law. Of course, science will be triangle even is equals two 2.5 common vehicles to 1.8 and Steve next to 0.9. By using local science, we can tie it to sign close to B squared plus B squared minus a squared divided by UBC. Now, with the substitute developed there 1.8 square plus 0.9 square minus 2.5 square, divided by two multiplied by 1.8 multiplied by 0.9 sold. In this, we get equal finding work minus school 0.2 divided by three point before Wang the least wanted 0.77 babies. Not again. By using law for science. Can I assign me close to a square B squared minus B squared, divided by Who is he now? We will search for two values here, 2.5 square plus 0.9 square minus 1.8 with the weighted by to Medicare by 2.5, multiplied by 0.9 consulting this week, and I would be too for finding words 3.2, divided by 4.5 The angle beast 31.91 degrees. No, he did find Anglesey by using local science for science B squared plus B squared minus the square. Delighted by Webby 1.8 where plus 2.5 square. My enough little 0.9 square, divided by two, multiplied by 1.8 by two by about 2.5. Involving this, they get to sign in west 8.6 ft, divided by nine The English East, 10.2 degrees. Thank you.

Mhm. In this question, we are going to solve the oblique triangle, starting with the law of co signs. Typically when we are given three sides of a triangle, we want to find the largest angle. First. The largest angle would be opposite the longest side. So we're going to solve for angle. See using the law of co signs and I will plug in the values we've been given 16 squared equals a squared plus B squared minus two times a times B times co sign of C. Now, let's do some of the math. And we want to be careful to follow order of operations. Start with 16 squared on the left. Okay. On the right, let's add 10 squared plus 12 squared. Let's multiply two times 10 times 12. Next let's subtract 244 from both sides, divide both sides by negative 2 40. Mhm and take the inverse co sign of both sides. To find the measure of angle, see Anglesey will have a measure of 92.87 degrees. Now that we know one angle and it's opposite side. We can use law of sines to find another angle. Since I'm looking for an angle let's say angle A. I would put sign of A. In the numerator over side A equal to sign of angle see mm over side see multiply both sides by 10 and now take the inverse sine of both sides to find the measure of angle A. Yeah, the measure of angle A will be 38.63 degrees. Finally, we can find the measure of the third angle by subtracting from 1 80 the measures of angle see and measure A. And we will find that the measure of angle be is 48.51 degrees. Yeah. Again, when we're given three sides of an oblique triangle, we can find the missing angles. Using the law of co signs. Start with the largest angle first, and finally, if you wanted to double check some things to make sure math turned out okay, add these angles up and they should add up to approximately 180 degrees. We rounded each of those. They might not be exactly 180 degrees, but pretty darn close. The triangle has been solved.

We are going to solve an oblique triangle using the law of co signs at least. That's what we'll start with. And that's because we've been given the three sides of the triangle when we have been given the three sides of the triangle, we want to solve for the largest angle first, which would be opposite the longest side. So let's find the measure of angle. See first using the law of co signs, I'm going to substitute in C squared equals a squared plus B squared minus two times a times b times co sign of angle. See And that's what we're solving for. Let's do some of the math. Eight square to 64. Next I want to do seven squared plus three squared to get 58 then two times seven times three. Yeah. Which is a coefficient of co sign of C. Subtract 64 minus 58. Yeah. To get six and divide both sides by negative 42. Okay, Finally take the inverse co sign of both sides. Mm. Yeah. Oh. And you'd get the measure of angle see to equal 98.21 degrees. Now that we know an angle and it's opposite side. We can use the law of sines to find our next missing angle. You can find angle or angle B. That is your choice. Let's find angle A. I would set up law of sines as sign of angle A over side A equal sign of angle see over side, see multiply both sides by seven and take the inverse sine 98.21. The inverse sine will tell us that the measure of angle A is 60 degrees. Yeah. It's finally, we can find the measure of the third angle by subtracting the first two from 1 80. Yeah. Mhm. And that tells us that the measure of angle B is 28.79 degrees. To do some double checking. You can always add up real quick the measure of all three angles, because certainly they should add to 1 80. In this case they do again as we are given three angles of an oblique triangle. You will use the law of co signs to find the largest angle first, and then the law of sines to find a second angle and third subtract the first two angles from 1 80 to get the measure of the third angle, and the triangle has been solved.

In this question, we are going to solve an oblique triangle using the law of co signs. Starting with the law of co signs. And that's because we've been given the length of two sides and the measure of the included angle side, angle side. Let's adapt the law of co signs to fit are given information. Okay? We've been given angle A. So I'm going to start my law of co signs with A squared equals B squared plus c squared minus two times B. Times C. Times co sign of angle A. Now we substitute in the values that we've been given, B squared plus C squared minus two times B times C. Times co sign of angle A. In fact, let me go ahead and take the square root in my next step, 15 squared 30 squared two times 15 times 30. And you can simplify some more if you'd like or you can put everything straight into your calculator as you see it. And you will find that the length of side A is 18.59 Now that we know an angle and it's opposite side. We can solve for one of the other missing angles by using the law of sines. If I wanted to find angle B, I would set up law of sines to say sign of angle be over side B equal sign of angle A. Yeah over side A. Multiply both sides by 15 and to find angle B. Take the inverse sine of both sides. Make sure you use parentheses properly. Okay? And you will get 23.79 degrees for the measure of angle be 23.79 Finally, we can find the third angle by subtracting the first two angles from 1 80. The measure of angle see is a result of 180 degrees minus the 30 degree angle that was given minus the 23.79 degree angle that we found. And the measure of angle see is going to be 100 and 26.21 degrees. And as a quick check, something is wrong. If you're three angles does not do not add up to 1 80 they should add up to 1 80 here. They do. So we solved for side angle side using the law of co signs, finding the measure of the side opposite the given angle first, the triangle has been solved.


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