1. 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

2. 1) I'm assuming that B lies on the positive side of the x-axis.

$\displaystyle tan 30=\frac{OB}{AO}$
$\displaystyle \frac{1}{\sqrt3}=\frac{OB}{AO}$
$\displaystyle \frac{1}{\sqrt3}=\frac{OB}{25}$
$\displaystyle OB=\frac{25}{\sqrt3}$
So the coordinates of B are ($\displaystyle \frac{25}{\sqrt3}$, 0).

3. Originally Posted by alexmahone

[snip]

$\displaystyle tan 30= \frac{OB}{AO}$
$\displaystyle \sqrt3=\frac{OB}{AO}$
Could you elaborate?

my calculator is different
$\displaystyle \sqrt{3}= 1.732050808...$
$\displaystyle \tan 30 = 0.577350269$
$\displaystyle \tan 60 = 1.732050808$

$\displaystyle tan 30 = \frac{1}{\sqrt3}$