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25 October, 19:47

A flagpole which is 40 feet high casts a shadow on level ground. At the time when the shadow is 30 feet long, the angle that the sun makes with the horizon is changing at a rate of 15o per hour. Find the rate of change in the length of the shadow at that same time.

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  1. 25 October, 20:04
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    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
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