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13. Solve triangle ABC if a = 9.47,b=15.9,and € =21.1. Round angle measures to the ncarest degree:14Solve the right triangle ABC (angle € is the right a...

Question

13. Solve triangle ABC if a = 9.47,b=15.9,and € =21.1. Round angle measures to the ncarest degree:14Solve the right triangle ABC (angle € is the right angle) if b = 9.4 andc = 14.5

13. Solve triangle ABC if a = 9.47,b=15.9,and € =21.1. Round angle measures to the ncarest degree: 14 Solve the right triangle ABC (angle € is the right angle) if b = 9.4 andc = 14.5



Answers

In $14-19,$ find, to the nearest tenth, the measure of the third side of each triangle.
In $\triangle A B C, b=12.4, c=8.70,$ and $\mathrm{m} \angle A=23$

We're getting a phone pieces of reparation and were asked to find what B is equal to. So we know you think of this A. C. You can think of this as a sonar, not B squared is equal to a squared plus a C squared. Nice to terms a toasty times to co sign of three so you can be is equal to the square root Those six points you four squared plus 2.35 squared Those two times 6.24 homes cheer. Put 35 tons of co sign 1 15 What will get us to be approximately equal to 7.5.

You're on the phone pieces of a racially asked policy is equal to know that. See scored people to a square plus B squared minus two times a comes to be to co sign of C so you get C squared is equal to 62.5 squared plus 4 4.7 squared to get US 5904.34 minus a cheer times 60 t point for our terms 44.7, which will get US 5587.5 tonnes of co sign of 133. So we know see single to square right of 5800 before but before minus 54th blackouts and 587.5 co sign of 100 dirty sweet. So if we put that in, we get C is equal to approximately 98.6 as cancer

In order to solve for question number 16 1st we're going to start by finding out what is the measure off the angle. See, we're going to use the fact that the sum of the angles decided triangles equal 280 decree. So we're going to say that measure of angle sees equal 280 minus two, some off the other two and goes that your 22 95 degrees? I'm not going to give us 63 degree as the measure of angle. See, now that we have them a measure of angle see, we could actually draw the triangle. So first we can start by drawing the line with 420 units as his measure. And that's going to be the side eight. We know that side days between the angles B and C. So now we know what is a measure of angles B and C so we could draw them if you know that measure of angle B is equal to 95 degrees. So we make a line such as this that makes the 95 degree angle with side A. And then we know that the a measure of angles sees actually equal to 63 degree because we have fallen out. So we make a line such as this that makes a 63 degree angle with side eight on the points that the two lines intersect is going to be angle A. We know that the measure off it is equal to 22 degree. So now we have sketched the triangle, and we're gonna use the love. So in order to find the elements that are missing eso we're going to say that sign off 22 degree over the measure, off the side of which is opposite to it. In this case, 420 is equal to shine off 95 degree over the opposite leg, which in this case is equal to be. And we're gonna have signed off 63 degree, uh, Teoh measure over the measure off the opposite leg, which, in this case, it's C. And that's gonna be the loft sign. Apply for this triangle so we could find B and C the missing elements very easily. B is going to be called to 420 multiplied by sine off 95 degree over. Sign off 22 degree and that's going to give an approximation as 1116.9 and C is going to be equal to 420 a multiplied by sine off 63 degree over. Sign off 22 degree again, and that's going to give us an approximation off 999 units. So we sketched it of triangle, and we have found the different measures that were missing from it. In order to solve the triangle, such as the measure of angle, see the measure of Side B and the measure off site C.

Okay, so we are provided with these measurements here, and we are asked to determine the number of possible triangles for these measures and then find the measures of the three angles for each possible triangle, and they just want us to express the measurements in the nearest degree. So let's start with a lot of science. I have sign of a Oh, oops, just kidding. I have a over sign A is equal to see over Sign. See, I'm, like, sort of drew a little bit of what we've got here. So I have a measurement of sea at 150 then they just put me here and a there, and I have 10 is opposite, See, Right, cause that's a length here and opposite a is nine. And so here I've got nine over Signed A is equal to 10 over sign of 1 50 And so when I cross multiply and then divide by 10 I get that sign. A is equal to nine times SAT ops. Let's plug in for sign of 1 50 So when we use our unit circle, we get sign of 1 50 is 1/2 and then that's divided by the 10. And so here nine times 1/2 is 4.5 and then divided by 10. You just move the decimal point, Phil, left by one. And so here, When we take the inverse sine, we get the measurement of angle A to be about 27 degrees. OK, so using the rules that were provided, it were told that if these two angles here when we have an obtuse angle, which is this angle here which is greater than 90 when we haven't obtuse angle which is what this looks like here and Islam Aziz two angles when they add up 1 50 plus, the 27 are less than 1 80 Then we do get one triangle. So this does work out and we have This is being 27 degrees. And so we just use the addition of these two. So that's 1 77 and subtract that from 1 80 I get that The measurement of Angles B is equal to three degrees


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