Answer: the distance is 3.49 units
Explanation:
There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.
When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:
x = R*cos(θ)
y = R*sin(θ)
Then we have:
(7,217pi/180 )
R = 7
θ = (217/180)*pi
x = 7*cos( (217/180)*pi) = -5.59
y = 7*sin( (217/180)*pi) = -4.21
So this point is (-5.59, -4.21) in rectangular coordinates.
And the other point is (5,-23pi/36 )
R = 5
θ = -(23/36)*pi
x = 5*cos( -(23/36)*pi ) = -2.11
y = 5*sin( -(23/36)*pi ) = -4.53
So this point is (-2.11, - 4.53)
Then the point distance between those points is:
D = I (-2.11, -4.53) - (-5.59, -4.21) I
D = I (-2.11 + 5.59, -4.53 + 4.21) I
D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49