I have no idea how to do this

Question

Find the value of the angle theta in degrees rounded to the neartest tenth of a degree.

I have no idea were to start...

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Answer 1

the circles go to the top and there measurements i included in the pictures and there are right angles

Answer 2

if you don\'t understand the problem i tried to draw it in paint

Answer 3

Are you sure the 2 circles don't touch ?

If the do, it is an easy problem.
draw a line from the vertex through the two centres.
Let the distance between the vertex and the centre of the smaller circle be x
then the distance from the vertex to the centre of the larger circle is x+6

sin (theta/2) = 2/x
sin (theta/2) = 4/(x+6)
then 2/x = 4/(x+6)
which solves for x=6

then sin (theta/2) = 2/6
theta/2 = 19.47º
theta = 38.942º or 38.9º to the nearest tenth.