# Graphic Artist (Vector Problem)

1. Sep 26, 2009

### Hi.O303

1. The problem statement, all variables and given/known data
The origin ( 0 , 0 ) is at the upper left corner of the image, the +x-axis points to the right, the +y-axis point down. Distances are measured in pixels. The artist draws a line from the pixel location ( 10 , 20 ) to the location ( 210, 200 ). She wishes to draw a second line that starts at ( 10 , 20 ), which is 250 pixels long, and is at angle 30 degrees clockwise from the first line.
(a) At which pixel location should this second line end? Give your answer to the nearest pixel.

2. Relevant equations
a^2+b^2 = c^2

3. The attempt at a solution
First to get the angle of the first line : I subtract 210 - 10 = 200 = x , 200 - 20 = 180 = y .
Then to get the angle of the first line I take arctan ( 180 / 200 ) = 41.9872° , So the angle of the second line must be 71.9468° . Then since the magnitude of the vector is 250, to get the component vectors I just take
250sin(71.9872) = y = 237.7468 + 20 = 257.7468
250cos(71.9872) = x = 87.3073 + 10 = 87.3073
So I guess they want the area that is covered, which is
(87.3073² + 257.7468²) = 64146 pixels , but their answer is 87,258. Does anybody know how they could've gotten this answer?