Question

What is the distance between the following polar coordinates?: `(2,(7pi)/4), (7,(7pi)/8)`

Answer 1

The distance is `~~ 8.88`

Explanation:

The two points and the origin form a triangle with sides, `a = 2, b = 7,` and the angle between them `C = (7pi)/4 - (7pi)/8 = (7pi)/8`. Therefore, the distance between the two points will be the length of side, c, and we can use the Law of Cosines to find its length:

`c = sqrt(a^2 + b^2 - 2(a)(b)cos(C)`

`c = sqrt(2^2 + 7^2 - 2(2)(7)cos((7pi)/8))`

`c ~~ 8.88`