Can the angle take any value?

An isosceles trapezium has a perimeter of \(80\), and an area of \(250\). Let \(\theta\) be the angle between any two adjacent sides. If the minimum of \(\sin\theta\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\)