Question
A streetlight is mounted on top of a 15 ft. pole. A 6-ft tal man walks away from the pole along straight path. How long is his shadow when he is 40 ft from the pole?
Answers
drwls
Consider the two similar right triangles formed. One has perpendicular sides 15 and 40 +x. The other has corresponding perpendicular sides 6 and x. The shadow length is x.
15/(40+x) = 6/x
(40+x)/x = 15/6 = 2.5
40/x + 1 = 2.5
40/x = 1.5
x = 26.67 feet
15/(40+x) = 6/x
(40+x)/x = 15/6 = 2.5
40/x + 1 = 2.5
40/x = 1.5
x = 26.67 feet
Reiny
did you make a sketch?
Let the length of his shadow be x
I have 2 similar triangles, so use a proportion:
6/x = 15/(x+40)
cross-multiply
15x = 6x + 240
9x = 240
x = 240/9 = 80/3 ft or 26 2/3 ft
Let the length of his shadow be x
I have 2 similar triangles, so use a proportion:
6/x = 15/(x+40)
cross-multiply
15x = 6x + 240
9x = 240
x = 240/9 = 80/3 ft or 26 2/3 ft
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