Anita is 5 ft. tall and walks at the rate of 4 ft./sec away from a street light with its lamp 12 feet above ground level. Find an algebraic representation for the length of Anita's shadow as a function of time, t.
Express the distance, D, between the street light's lamp and the tip of Anita's shadow as a function of time, t.
I tried drawing a picture using a triangle, but cannot get it at all. Any ideas?
Would this be rite?
A(lamp)
|
| ...................... C (anita)
12.................... |
| ...................... 5
| .......................|
B ....... x ......... D ........................................ H (Tip of head)
Join RAY> ACH
anita moved distance x in time (t)
x = speed * time = 4t
> let DH = y = length of shadow
> angle AHB = CHD = p
tan p = 12/(4t+y)
tan p = 5/y
5/y = 12/(4t+y)
5(4t+y) = 12 y
7y = 20 t
y = length of shadow = 20t/7 >>>>>>>>>>>>>>
--------------------------------------...
D = BH = x + y
D = 4t + 20t/7
D = [28t + 20t]/7
D = 48 t/7
I know that I'm triple posting, but my edit button does not seem to work. When I press it, it doesn't allow me to edit my previous posts.
Anyways. for the distance in the second part of the problem, would it be the hypotenuse of the triangle instead of the bottom leg of the triangle as it said to find the distance between the street light's lamp and the tip of the shadow as a function of time.
That means would would have to use pythagorean theorem with [tex] y = \frac {20t}{7}[\math] (length of shadow) and 12 as they are the length of the sides of the assumed triangle rite?
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