Given the radius of a circle and the tangent how doe I find the circumference of the arc

Question

I am being asked to find the circumference of an arc and given the radius and the tangent.

Answer 1

If by the tangent is meant the tangent t of the angle θ of the arc, then t=tanθ and θ=tan^-1(t) or arctan(t).

The length of the arc s=rθ where r is the radius of the circle containing the arc:

s=rtan^-1(t).