# How do I find the distance between polar coordinates (3, 60^circ) and (5, 145^circ)?

Angle between them is ${85}^{o}$ one of the length is 3, and other is 5.. Therefore by cosine rule
${a}^{2} + {b}^{2} - 2 a b \cos \theta = {c}^{2}$
$\implies {9}^{25} - 2 \cdot 3 \cdot 5 \cdot \cos 85 = {c}^{2}$
$\implies 34 - 2.614 = 31.386 = {c}^{2}$
$\implies c = \sqrt{31.386} = 5.602$