# What is the distance between polar coordinates (2, 120^circ) and (1, 150^circ)?

Jul 9, 2018

color(brown)("Distance " d = 1.2393

#### Explanation:

$d = \sqrt{{r}_{1}^{2} + {r}_{2}^{2} - 2 {r}_{1} {r}_{2} \cos \left({\theta}_{1} - {\theta}_{2}\right)}$

$\left({r}_{1} , {\theta}_{1}\right) = \left(2 , {120}^{\circ}\right) , \left({r}_{2} , {\theta}_{2}\right) = \left(1 , {150}^{\circ}\right)$

d = sqrt(2^2 + 1^2 - 2 * 2 * 1 * cos (120-150)

$d = \sqrt{5 - 4 \cos \left(- 30\right)} \approx 1.2393$