What is the distance between the following polar coordinates?:  (4,(5pi)/3), (3,(7pi)/6)

Dec 10, 2017

$\implies 5$

Explanation:

Here I have drawn an image to show the polar coordinates and there respective lengths

We are trying to find $x$

We see that $\alpha = \frac{5 \pi}{3} - \frac{7 \pi}{6} = \frac{\pi}{2}$

Now we can use the rule of cosines, but as $\alpha$ is a right anlge we can just use pythag:

${x}^{2} = {3}^{2} + {4}^{2}$

$\implies x = \sqrt{9 + 16}$

$\implies x = \pm 5$

Must be postive as lengths can be negative:

$x = 5 =$ our length