what is the measure of qr to the nearest hundredth of a centimeter?

For this question, you need to decide whether to use sin cos or tan.
You have the hypotenuse and Ф but you need to find the opposite side.

For those reasons you would use sin, as it has all three in its triangle,
The equation for opposite = sinФ * hypotenuse
So sin49 * 12.38 = 9.3cm.

The answer is 9.3cm.

Hope this helps.