SOLUTION: The sun is setting at a steady rate of 0.25� per minute (assume that the sun sets perpendicular to the horizon). A 19m pole casts a shadow on the ground and the shadow is lengtheni

Question 1105906: The sun is setting at a steady rate of 0.25� per minute (assume that the sun sets perpendicular to the horizon). A 19m pole casts a shadow on the ground and the shadow is lengthening as the sun sets further. How fast is the shadow lengthening at the moment when it is 35 meters long?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
tan theta = 19/35 = 0.5429 and theta = tan^(-1) 0.5429 = 28.4975 approximately 28.5 degrees
:
tan theta = 19/x
:
x = 19/tan theta
:
take the first derivative
:
dx/dt = (-19/sin^2 theta) * d(theta)/dt
:
we know d(theta)/dt = -0.25 degrees/minute and dx/dt is how fast the tip of the shadow is moving
:
dx/dt = (-19/0.2277) * (-0.25) = 20.86 m/minute
:

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