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A man standing 3 ft from the base of a lamppost casts a shadow 4 ft...?
A man standing 3 feet from the base of a lamppost casts a shadow 4 feet long. If the man is
6 feet tall and walks away from the lamppost at a speed of 270 feet per minute, at what rate
will his shadow lengthen?
I've tried using similar triangles and then taking the derivative but the answer I'm getting doesn't match the answer key. Help please?
2 Answers
- BryceLv 75 years ago
6/4=L/7; L=10.5 ft The lamppost is 10.5 ft high.
x=the length from the lamppost to the man, and y= the length of the man's shadow.
y/6=(x+y)/10.5; 10.5y=6x+6y; y=(4/3)x
dy/dt=(4/3)dx/dt= (4/3)*270= 360 ft/min
