A street light is at the top of a 11 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 feet from the base of the pole

8.8ft/s

Step-by-step explanation:

Height of pole=11 foot

Height of man=6  foot

Let x be the distance of man from the pole and y be the distance of tip of shadow from the base of the pole.

Two right  triangles are similar then the ratio of their corresponding sides are equal

Differentiate w.r.t t

Hence, the tip of her shadow is moving at the rate 8.8ft/s when she is 45 feet from the  base of the pole

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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