Three vectors A, B and C are such that
A = B + C and their magnitudes are 5, 4 and 3 respec-
tively. Find the angle between A and C.

Please answer with explanation

Since the magnitudes satisfy the identity for right triangles

we deduce that B and C are perpendicular, and that ABC is a right triangle (see picture).

So, we can get the angle between A and C using the sine theorem:

And we have

So, we have

Which implies

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