Answer: The rate = 8.5 ft/h
Step-by-step explanation:
Since we are going to need to differentiate to find the rate of change of θ we need to express it in radians rather than degrees.
Therefore, 15 degree per hour will be expressed as
15° × π/180 = 0.2618rad/hour
Using trigonometry function to find Ø
Tan Ø = 40/30 = 1.333
Ø = 53 degree
Convert it to radian
Ø = 0.93 rad
The changing at a rate of 15o per hour will be
Rate = radian/ time
0.2618 = (0.93 -0)/t
t = 0.93/0.2618
t = 3.5 hours
The rate of change in the length of the shadow at that same time will be:
Rate = 30/3.5 = 8.5 ft/ hour
