# What is the distance between the following polar coordinates?:  (7,(3pi)/4), (3,(pi)/8)

##### 1 Answer
Jul 11, 2017

$\approx 8.61$

#### Explanation:

You can use the Law of Cosines.

If you plot the polar coordinates and draw lines from the origin to the points, you will have 2 sides of a triangle. The 3rd side will be the distance between the 2 points.

Find the angle $C$:

$\frac{3 \pi}{4} - \frac{\pi}{8} = \frac{6 \pi}{8} - \frac{\pi}{8} = \frac{5 \pi}{8}$

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$
${c}^{2} = {7}^{2} + {3}^{2} - 2 \left(7\right) \left(3\right) \cos \left(\frac{5 \pi}{8}\right)$
${c}^{2} = 58 - 42 \cos \left(\frac{5 \pi}{8}\right)$
${c}^{2} \approx 74.07$
$c \approx 8.61$

You can also solve this problem by converting the polar coordinates to rectangular coordinates and using the distance formula.