 In this video we provide the solution to question number 11 for practice exam number 3 for math 1060. In which case we're given a triangle, A, B, C, and we're asked to solve for this triangle. The information we know is that we know angle A is 30 degrees, angle B is likewise 30 degrees, and the side opposite angle A, which we call lila, is 8 centimeters long. Notice this is a situation we have angle angle side, which is an appropriate place to use the loft signs. Also, we can see here that we have an angle opposite side pair in AOS. So the loft signs is what we're going to want to use here. So the first thing we want to do is probably figure out what angle C is going to be here, right? So the measure of angle C is going to equal 180 degrees minus the measure of angle A, which is 30, minus the measure of angle B, which is likewise 30. 30 and 30 come together to give me 60, of course. And if you take that away from 180, you're left behind at 120 degrees. So that's going to be the measure of angle C, 120 degrees, like so. Next, we're going to use the loft signs to find the missing sides, always comparing to the AOS that we know, which is the A1 there. So to find lila B, we're going to use the equation lila B over sine B is equal to lila A over sine A. Plugging the information we know. Well, actually, we'll times both sides by sine of B. So we get that little B equals A sine of B over sine of A here. And for which case we're going to get that little A is 8. Sine of B is sine of 30 degrees, like so. And sine of A is actually also, sorry, sine of A is also 30 degrees. So you can sine of 30 degrees. Sine of 30 degrees is one half. We don't even need a calculator for that. But since it's both the same, those are going to cancel out and we get 8 right here. So A is also 8. A is 8. We knew that B is 8 as well, 8 centimeters for a little B. Now that might not be too surprising when you look at that hindsight. Notice you have 30 and 30. This is an isosceles triangle. So the two angles are congruent. The opposite sides are also going to be congruent to each other. It's an isosceles triangle. This diagram is not drawn to scale. You should never expect them to be. Define the remaining side, little C. We need to do another law of sine. So we're going to use A again. If you want to use B, you could. But I'm just going to stick with A. Little C over sine of C is equal to little A over sine of A. This suggests that little C is equal to A times sine of C over sine of A. For which case we get A is 8. Sine of 120 degrees, like so. Over sine of 30 degrees. So let's think about this for a second. 120 degrees actually references 60 degrees. It's the reference angle of 120 is 60 degrees. Basically saw that from above right here. Anyways, so that means sine of 120 is the same thing as sine of 60 over sine of 30. And again, you do have a calculator you can use, but these are all special angles. No calculators actually needed here. We get that sine of 60 degrees is root three over two. Sine of 30 degrees is one half. So if we times top and bottom by two, we'll end up with eight times the squared three centimeters. And that's the exact value there. If we want an approximation because you do have a calculator, you could have approximated 13.856 centimeters. That also would be acceptable. But exact answers are definitely preferred on these ones. And so we see the exact value here would be eight times the square root of three. And that then finishes this oblique triangle that we've now solved.