Question

What’s the distance between polar coordinates (3,−60°)and(−5,105°) ?

Answer 1

2 Units

Explanation:

THere may be easier ways to do it, but I would just convert them to rectangular and find the distance between those.

(3, -60) becomes (3cos(-60), 3sin(-60)) = (3/2, -3*sqrt(3)/2)

(-5, 105) becomes (-5cos(105), -5sin(105)) = (5/2, -5sqrt(3)/2)

Now just use the distance formula, or in other words think of the two points as being connected by a horizontal and vertical line to form a right triangle. The idea is to find the hypotenuse of that right triangle.

sqrt((3/2 - 5/2)^2 + (-3sqrt(3)/2 + 5sqrt(3)/2)^2)

sqrt((-2/2)^2 + (2*sqrt(3)/2)^2)

sqrt(1 + 3)

sqrt(4)

2