I just want to check if my reasoning and answer are correct. The question is:

A rocket is launched straight up, and it's altitude is given by after seconds. You are on the ground 300m from the launch site watching the rocket going up. The line of sight from you to the rocket makes and angle with the horizontal. By how many radians per second is changing 10 seconds after the launch?

My reasoning is as follows:

Need to find

, so .

, so .

Remembering ,

Also, since , when .

Therefore,

So using Chain Rule:

Any help will be much appreciated.