# What is the distance between the following polar coordinates?:  (2,(7pi)/4), (7,(7pi)/8)

Nov 15, 2016

The distance is $\approx 8.88$

#### Explanation:

The two points and the origin form a triangle with sides, $a = 2 , b = 7 ,$ and the angle between them $C = \frac{7 \pi}{4} - \frac{7 \pi}{8} = \frac{7 \pi}{8}$. Therefore, the distance between the two points will be the length of side, c, and we can use the Law of Cosines to find its length:

c = sqrt(a^2 + b^2 - 2(a)(b)cos(C)

$c = \sqrt{{2}^{2} + {7}^{2} - 2 \left(2\right) \left(7\right) \cos \left(\frac{7 \pi}{8}\right)}$

$c \approx 8.88$