need direction

[smsuski]

This is the problem:
a 6 foot tall man is standing near a 15 foot lampost.
a) express the length of his shadow as a function of his distance from the lampost. Be sure to define your variables.
I know I have 2 rt triangles.
1) a=6, b=distance from man to end of shadow
2) a=15, b=distance from pole to man + distancefrom man to end of shadow
I also know that a^2+b^2=c^2 and that triangle 1 is a propotion of triangle 2.
would I use a rate of change function?

 

[arthur ohlsten]

1. sketch 2 perpindicular lines "x" distance apart on a horizontal line. make one 15 units high and the second 6 units high. pass a straight line from the top of each line to the base line.
2. mark the base angle @ , the distance along the horizontal from the base of each line x
3. mark the distance from the base of the 6 unit high line to the intersection of the slant line and the base s , for shadow length
4. from the two right triangles:
Tan @ = 15/[s+x] and Tan @ = 6/x
5. setting the tan equal to each other
15/[s+x] = 6/x solve for s
15x =6s+6x
s= [9/6]x
s= 1.5 x answer
Arthur