Jl is a common tangent to circles m and k at point j. if angle mlk measures 61ᵒ, what is the length of radius mj? round to the nearest hundredth. (hint: show that triangles lmj and lkj are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)

In the problem of insufficient data quantities. I can get a general  solution.We know that tangent to a circle is perpendicular to the radius at the point of tangency. It's mean that triangles LJM and LJK are rights.

Let angle JLK like X.

So, angle JLM=61-x.

And it's mean that by using right triangle trigonometry 

Radius MJ = LM*cos(61-X)

X> -2 is the simplified version.