The one angle given is 45 degrees. It is also understood that the red square there in the corner indicates a right angle, measuring 90 degrees. By the triangle angle-sum theorem, all the angles in any triangle add up to equal 180. That means that the angle that's not yet been labeled measures 180-45-90 which is 45 degrees. So this is a 45-45-90 special right triangle. This type of triangle has a Pythagorean triple assigned to it. It is, in terms of x, [tex](x,x,x \sqrt{2}) [/tex]. In terms of numbers it is [tex](1,1, \sqrt{2}) [/tex] with the square root of 2 being the largest measurement and therefore the hypotenuse. The sin ratio uses the side opposite the reference angle over the hypotenuse. So for us in this particular triangle, the sin of 45 is going to be the side opposite the 45 degree reference angle over the hypotenuse. That ratio then is [tex] \frac{1}{ \sqrt{2} } [/tex]. Rationalizing the denominator gives you [tex] \frac{ \sqrt{2} }{2} [/tex]. I cannot see all your choices in the pic you provided so I can't tell you what letter is associated with that answer. But that's the one you're looking for!
