# What is the distance between the following polar coordinates?:  (11,(17pi)/12), (4,(pi)/8)

Jul 9, 2018

color(green)("Distance between the polar coordinates " ~~ 13.8047

#### Explanation:

Distance between tow points knowing the polar coordinates is given by the formula using cosine rule

d = sqrt(r_1 ^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_2 - theta_1)

$\text{Given } {r}_{1} = 11 , {r}_{2} = 4 , {\theta}_{1} = {\left(\frac{17 \pi}{12}\right)}^{c} , {\theta}_{2} = {\left(\frac{\pi}{8}\right)}^{c}$

d = sqrt (11^2 +4^2 - (2 * 11 * 4* cos ((pi)/8 - (17pi)/12))

$\textcolor{g r e e n}{d} = \sqrt{137 - 88 \cos \left(\frac{- 31 \pi}{24}\right)} \textcolor{g r e e n}{\approx 13.8047}$