 Consider the figure provided where we have a right triangle given right here as the A, C, D triangle, where D is a right angle. And suppose that this triangle also shares points with the circle, a circle centered at point C, and so that B, C, likewise C, D are both radii of that circle. And so given this information where B sits in between A and C, B is not a vertex of the triangle, but it is on the circumference of the circle. So given this diagram, can we determine the missing side, A, B? That is, can we find the distance here of X? Okay, so the distance between A and B. So you'll notice that this value X is not the side of a triangle, but it is part of the side of the triangle. So in particular, if we put this together, if we take A, C, so let's be specific here, the distance A, B is equal to X. A, C is going to equal X plus 18, where you'll notice that 18 is the radius of the circle. We know that the measure of angle A is 35 degrees. How can we connect that to these variables X? Well, because we have a circle, all of the radii are the same length, which is 18. So in particular, the other side, C, D, since it's a radius of a circle, it will be the same distance as B, C, which means this here is 18. So we have this angle A for which we know its opposite side is 18, and we know the hypotenuse is X plus 18. So using the sine ratio, sine of A, is going to equal here, C, D over A, C. And putting the information in there, we have sine of 35 degrees. This is equal to 18 over X plus 18. So we get this ratio right here. We need to solve this equation for X. So the first thing to do is clear the denominators. You end up with X plus 18 times sine of 35 degrees. I'm going to postpone computing the sine of 35 degrees until much later on in this problem here. Because again, we want to solve for X. We could distribute sine of 35 degrees right here. We'll get X times sine of 35 degrees. Always remember to put the degree symbol. If you don't put the degree symbol, it actually suggests that you're doing 35 radians, which is a very different angle measure. We also get 18 times sine of 35 degrees. This is equal to 18. So I'm going to subtract 18 sine 35 degrees from both sides of the equation. I get X times sine of 35 degrees. This is equal to 18 minus 18 sine of 35 degrees. And then divide both sides of the equation by sine of 35 degrees. We end up with X equals. I'm also going to factor out the 18 on the right hand side. So you get 18 times 1 minus sine of 35 degrees. And this sits above sine of 35 degrees. So this is the exact answer of this problem. You might be tempted because there's a sine of 35 degrees on both sides, on both the top of the bottom. You might want to cancel it out. You can't cancel out exactly. If you leave the numerator factor and you broke it up, this is the same thing as 18 over sine of 35 degrees minus 18. So if you separate it into two fractions, the sine of 35 degrees would cancel on top and bottom. So depending on how you solve this equation, there's more than one way of doing it. You could either get this or this as your exact answer. The two things are equivalent to each other. So whichever of the two forms you came up with doesn't really matter. Put them into your calculator. The second form seems a little bit easier to enter into your calculator. But nonetheless, you put into your calculator and you get as your estimate 13. That is if we round to the nearest integer. The distance of X would be approximately 13.