Answer
The distance between the two points is $~~\sqrt{r_2^2+r_1^2-2r_1~r_2~cos~(\theta_1~-\theta_2)}$
Work Step by Step
We can find the Cartesian coordinates of the first point:
$x_1 = r_1~cos~\theta_1$
$y_1 = r_1~sin~\theta_1$
We can find the Cartesian coordinates of the second point:
$x_2 = r_2~cos~\theta_2$
$y_2 = r_2~sin~\theta_2$
We can find the distance between the two points:
$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d = \sqrt{(r_2~cos~\theta_2-r_1~cos~\theta_1)^2+(r_2~sin~\theta_2-r_1~sin~\theta_1)^2}$
$d = \sqrt{(r_2^2~cos^2~\theta_2-2r_1~r_2~cos~\theta_1~cos~\theta_2+r_1^2~cos^2~\theta_1)+(r_2^2~sin^2~\theta_2-2r_1~r_2~sin~\theta_1~sin~\theta_2+r_1^2~sin^2~\theta_1)}$
$d = \sqrt{(r_2^2~cos^2~\theta_2+r_2^2~sin^2~\theta_2)+(r_1^2~cos^2~\theta_2+r_1^2~sin^2~\theta_1)-2r_1~r_2~(cos~\theta_1~cos~\theta_2+~sin~\theta_1~sin~\theta_2)}$
$d = \sqrt{r_2^2+r_1^2-2r_1~r_2~cos~(\theta_1~-\theta_2)}$
The distance between the two points is $~~\sqrt{r_2^2+r_1^2-2r_1~r_2~cos~(\theta_1~-\theta_2)}$
