# What is the distance between #(3 , (3 pi)/8 )# and #(9, pi )#?

##### 2 Answers

#### Explanation:

The position vectors to the points are of lengths a = 3 and b = 9. The angle in-between is C =

Use the formula c =

#### Explanation:

To convert the polar coordinates to Cartesian coordinates, we use

#x = r cos(theta)#

#y = r sin(theta)#

The cartesian coordinate of

The cartesian coordinate of

We can use the Pythagoras Theorem to find the distance between the 2 points

#d = sqrt{(-9 - 3cos({3pi}/8))^2 + (0 - 3sin({3pi}/8))^2}#

#= sqrt{(81 + 9cos^2({3pi}/8) + 54cos({3pi}/8)) + 9sin^2({3pi}/8)}#

#= sqrt{90 + 54cos({3pi}/8)}#

#= 3sqrt{3sqrt{2-sqrt2}+10}#

#~~ 10.520#