# What is the distance between the following polar coordinates?:  (2,(5pi)/12), (1,(3pi)/12)

Apr 1, 2017

The distance is $\approx 1.239$

#### Explanation:

Use the Law of Cosines:

${c}^{2} = {a}^{2} + {b}^{2} - 2 \left(a\right) \left(b\right) \cos \left(A\right)$

where c is the distance between the two points $a = 2 , b = 1 \mathmr{and} \angle A = \frac{5 \pi}{12} - \frac{3 \pi}{12} = \frac{\pi}{6}$

${c}^{2} = {2}^{2} + {1}^{2} - 2 \left(2\right) \left(1\right) \cos \left(\frac{\pi}{6}\right)$

${c}^{2} \approx 1.536$

$c \approx 1.239$