If I said that the voltage was \$10\cos(100t)\$ and the current was \$5\sin(100t)\$, would you be asking about the phase angle? I mean; the phase angle (when not mentioned) is implicitly assumed to be 0° so there wouldn't be any worry there if it wasn't mentioned. Are you OK with that?
So, if both voltage and current are shifted by 60° (or any phase angle), does it really affect how you would answer the question? No, because both are time shifted by the same amount and, the load that converted the cosine voltage waveform into a sinusoidal current is still exactly the same.
With respect to what is the phase shift 60deg.
To answer your question; it matters not one bit what the 60° is relative to. And, it's exactly the same when phase angle is not mentioned (assumed to be 0°). Other (different) problems involving phase angle might require us to validly ask what it is respect to but not in this example.
And for the power calculation, I should just multiply the values of V
Unfortunately, the answers given are probably all wrong.
When we talk about voltages or currents and mention the "sin" or "cos" parts we are implying that the voltage or current is a peak value (not an RMS value). To calculate VI or watts we have to use RMS voltage and current values and, the apparent power for a 10 volt peak amplitude voltage and a 5 amp peak amplitude current is 25 VA. So, if the answers to the question are all using phasor notation (\$X\angle\$ for instance), \$X\$ should be an RMS value.