# What is the distance between the following polar coordinates?:  (7,(pi)/4), (8,(11pi)/8)

Sep 29, 2017

Distance is $14.71$

#### Explanation:

Polar coordinates $\left(7 , \frac{\pi}{4}\right)$ and $\left(8 , \frac{11 \pi}{8}\right)$ can be written in Cartesian coordinates as

$\left(7 \cos \left(\frac{\pi}{4}\right) , 7 \sin \left(\frac{\pi}{4}\right)\right)$ or $\left(\frac{7}{\sqrt{2}} , \frac{7}{\sqrt{2}}\right)$

i.e. $\left(4.95 , 4.95\right)$ and

$\left(8 \cos \left(\frac{11 \pi}{8}\right) , 8 \sin \left(\frac{11 \pi}{8}\right)\right)$

or 8xx(-0.3827),8xx(-0.9239)) or $\left(- 3.0616 , - 7.3912\right)$

Hence, distance between them is

$\sqrt{{\left(4.95 + 3.0616\right)}^{2} + {\left(4.95 + 7.3912\right)}^{2}}$

= $\sqrt{64.1857 + 152.3052}$

= $\sqrt{216.4909}$

= $14.71$