OEThe diagonal of the rectangle is the hypotenuse of a right triangle whose legs are the length and width of the rectangle. In this case, you are given the width and the diagonal. Plug these into the Pythagorean theorem to determine the length:
\(a^2+b^2=c^2\)
\(1^2+b^2=2^2\)
\(b=\sqrt{3}\)
The key to this question is recognizing that each of the triangles is a 30–60–90 triangle. Any time you see a right triangle and one of the sides has a length of \(\sqrt{3}\) or a multiple of \(\sqrt{3}\), you should check to see whether it is a 30–60–90 triangle. Another clue is a right triangle in which the hypotenuse is twice the length of one of the other sides. Now, in addition to the side lengths, you can fill in the values of the angles in this diagram. Angle x is opposite the short leg, which means it has a degree measure of 30. Similarly, 2y is opposite the long leg, which means it has a degree measure of 60:
2y = 60
y = 30
_________________