# coordinate geometry

• May 26th 2009, 09:48 PM
roja2006
coordinate geometry
1) A line with a y intercept at A(0,25) makes an angle of 30 degrees with the y axis as shown. What are the coordinates of B, the x intercept of the line?

2) C is the center of the circle that has x intercepts at the points A and B. The radius is 6 cm. The line OC is 10cm long and joins the origin to the center and makes an angle of 35* degree
with the x axis. CD is perpendicular bisector of AB. Calculate the length of the cord AB
• May 26th 2009, 11:15 PM
alexmahone
1) I'm assuming that B lies on the positive side of the x-axis.

$tan 30=\frac{OB}{AO}$
$\frac{1}{\sqrt3}=\frac{OB}{AO}$
$\frac{1}{\sqrt3}=\frac{OB}{25}$
$OB=\frac{25}{\sqrt3}$
So the coordinates of B are ( $\frac{25}{\sqrt3}$, 0).
• May 27th 2009, 04:02 AM
aidan
Quote:

Originally Posted by alexmahone

[snip]

$tan 30= \frac{OB}{AO}$
$\sqrt3=\frac{OB}{AO}$

Could you elaborate?

my calculator is different
$\sqrt{3}= 1.732050808...$
$\tan 30 = 0.577350269$
$\tan 60 = 1.732050808$
• May 27th 2009, 04:19 AM
alexmahone
I made a mistake
$tan 30 = \frac{1}{\sqrt3}$
Sorry.

Edit: Fixed my previous solution.