# What is the distance between the following polar coordinates?:  (10,(17pi)/12), (4,(15pi)/8)

Oct 5, 2017

Distance between two points is $D = 10.27$ unit

#### Explanation:

Polar coordinates of two points are ${r}_{1} = 10 , {\theta}_{1} = \frac{17 \pi}{12} =$

${255}^{0} \mathmr{and} {r}_{2} = 4 , {\theta}_{2} = \frac{15 \pi}{8} = {337.5}^{0}$

Cartesian coordinate of 1st point is ${x}_{1} = {r}_{1} \cos {\theta}_{1}$or

${x}_{1} = 10 \cos 255 \approx - 2.588 \mathmr{and} {y}_{1} = {r}_{1} \sin {\theta}_{1} =$

${y}_{1} = 10 \sin 255 \approx - 9.659 \therefore \left(- 2.588 , - 9.659\right)$

Cartesian coordinate of 2nd point is ${x}_{2} = {r}_{2} \cos {\theta}_{2}$or

${x}_{2} = 4 \cos 337.5 \approx 3.696 \mathmr{and} {y}_{2} = {r}_{2} \sin {\theta}_{2} =$

${y}_{2} = 4 \sin 337.5 \approx - 1.53 \therefore \left(3.696 , - 1.531\right)$

Distance between two points is

D=sqrt( (x_1 − x_2)^2 + (y_1 − y_2)^2) =

D=sqrt( (-2.588 − 3.696)^2 + (-9.659 +1.531)^2) :.

$D = 10.27$ unit [Ans]