Set up the equation:

(1.00) x sin(34.5) = (1.5) x sin (Theta₂)

Then, you rearrange the equation by dividing both sides by 1.5:

(1.00) x sin(34.5)/1.5 = sin (Theta₂)

Now, you evaluate everything on the left.

As long as your calculator is in degrees mode, when you use it to calculate the sin of 34.5, you get 0.566406237. Thus, you now have:

(1.00) x (0.566406237)/1.5

which works out to

0.37760415795

So

0.37760415795 = sin (Theta₂)

To solve for Theta₂, you take the inverse sin of both sides.

On a calculator, the inverse sin might be labeled sin^-1 or arcsin or asin. The inverse sin of 0.37760415795 is 22.1852574259, which is 22 to two significant figures. The inverse sin cancels the sin on the right, so:

22 = Theta₂