Calculus
posted by Jon .
A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the shoreline.
I need to show work, so formatting answers in this manner would be most appreciated. Thanks in advance! :) :)

Evaluate the limit as h > 0 of:
[tan (pi/6 + h)  tan(pi/6)]/h
I thought the answer was √3/3, or tan(pi/6, but apparently that is wrong, any tips here? 
Sorry, I mean to make a new question, disregard above 'answer'.

Gee, now you're going to make people who open this topic think the answer has already been provided. Thanks a ton...

You're a jerk.

tan(θ)=x/1
cos(θ)=1/sqrt(x^2+1)
sec^2(θ)=x^2+1
dθ/dt=3 rev/min=6π rad/min
x=tan(θ)
dx/dt=sec^2(θ) dθ/dt
At x=0.5 km
dx/dt=(0.5^2+1)*6π=23.6 km/min=1414 kph