1. ## Trig Brain Cramp

The problem says:

An airplane is flying on a horizontal path at a height of 3800 ft. At what rate is the distance s between the airplane and a fixed point P (on the ground) changing with respect to theta when theta equals 30 degrees? Express your answer in units of ft/degree.

I understand the problem, and got -13,163.2 feet/??? Here is my dilemma:

The answer key says that this answer is in ft/rad and that I need to convert it to ft/deg, which is approximately -230 ft/deg. My question: WHY? If I plug 30 DEGREES into my calculator and get -13,163.2 feet, isn't that in DEGREES? I know HOW to do the conversion. I am not clear on why. Help?

Jeannine

2. The answer key says that this answer is in ft/rad and that I need to convert it to ft/deg, which is approximately -230 ft/deg. My question: WHY? If I plug 30 DEGREES into my calculator and get -13,163.2 feet, isn't that in DEGREES? I know HOW to do the conversion. I am not clear on why. Help?
because the derivatives of the trig functions you have learned are only valid when $\theta$ is in radians ... substituting in 30 degrees at the end of the problem using degree mode in your calculator only gave a specific value of the trig ratio in your expression that determined the desired rate of change, you would have gotten the same result substituting in $\frac{\pi}{6}$ in radian mode.