Hello, gralla55!

Your book's answer is correct, but it's rather clumsy.

I would avoid those silly fractions . . .

And: .

Substitute: .

. . . . . . . . . .[1]

Back-substitute: .

is in a right triangle with: .

Hence: .

And: .

Substitute into [1]: .

. . . . . . . . . . . . .