Careful . . . 5-5-8 is not a right triangle.
. . But your game plan is correct.
The area of the intersection of two circles of radius 5 cm
which have their centres 8 cm apart is?
* : *
5* :3 *5
* α : *
* * * * * * * * *
A 4 4 B
I get a triangle with sides 5, 5, and 8.
We also get a couple of 3-4-5- right triangles.
I work out the angle between the 5 side and 8 side.
then times that by 2 to get the full angle.
Then use the formula: .
then times that answer by two to get the final answer (the interection)