<p>Answers are: 47. B, 38. D</p>
<p>If someone could explain these, that'd be awesome. Thanks! :)</p>
<p>For 47
The sum of the angles of a pentagon = 540. If you forgot this, observe that a pentagon can be viewed as 3 separate triangle (so 3 times 180 degrees). For a regular pentagon the angles are equal; so they are each 108 degrees. In particular angle AED is 108 degrees.</p>
<p>Since each side is 2, the point E has coordinates (3.0). Draw a line from D perpendicular to the x-axis. It intersects the x-axis at point F. Now look at triangle EDF. You need the length of EF, since when you add that to “3” you’ll get the x-coordinate of D. Note that ED = 2 since that is a side of the regular pentagon. The sides of a regular pentagon are equal.</p>
<p>Note that the angle DEF is 72 degrees (180 - 108), and that EF=2 x cosine (72) = .62. The x-coordinate of D = 3 + 0.62.</p>
<p>For 38
One circle is centered at (0,0) and it has radius 1. The second circle is centered at (SQRT(2), SQRT(2)) and it also has radius 1. Draw the two circles, and the line between their origins. They touch half way between the origin of the first circle, and the origin of the second circle. That point is (SQRT(2)/2, SQRT(2)/2) or (.71, .71)</p>