Hi

Im a bit confused on working out trig equations. I know all the rules, but something doesn't make sense to me.

There is a question in my excercise book, which i worked out and i ended up with having to solve:

Sin 5 = 117.8 / x

Using the normal rules of equations, i got

x sin 5 = 117.8

117.8 / sin 5 = x

x = 1351

But the book said to do:

117.8 sin 5 = x

x = 10.3

Im a bit confused on why this works. Surely you multiply by the the denominator. Any explanations?