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?
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
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
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To find the length of the man's shadow when he is 40 ft from the pole, we can use similar triangles.
Let's consider the triangle formed by the man, the pole, and his shadow. We have two similar right triangles: one formed by the man, his shadow, and the ground, and another formed by the pole, its shadow, and the ground.
In the triangle formed by the man, his shadow, and the ground, we can label the height of the man as 'h' and the length of his shadow as 's'. Since the triangle is similar to the one formed by the pole, its shadow, and the ground, we know that the ratios of the corresponding sides are equal:
h / s = (height of the pole) / (length of the pole's shadow)
h / s = 6 / 15
Simplifying the equation:
h / s = 2 / 5
Now, we can solve for the length of the man's shadow (s) when he is 40 ft from the pole, knowing that the height of the man (h) is 6 ft:
s = (h * (length of the pole's shadow)) / (height of the pole)
s = (6 * 15) / 5
s = 90 / 5
s = 18 ft
Therefore, the length of the man's shadow when he is 40 ft from the pole is 18 ft.