A girl 1.6 m tall, stands 3.6 m from a lamp post at night. Her shadow from the light is 0.9m long. How high is the lamp post?
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To find the height of the lamp post, we can use similar triangles since the girl's height and her shadow form a proportion with the lamp post's height and the length of its shadow.
Let's represent the height of the lamp post as "x" and the length of its shadow as "y".
According to the problem, the girl's height is 1.6 m, and her shadow is 0.9 m. The distance between the girl and the lamp post is 3.6 m.
Using the similarity of triangles, we can set up the following proportion:
girl's height / girl-to-lamp post distance = lamp post height / lamp post shadow length
1.6 m / 3.6 m = x / 0.9 m
To solve for x, we can cross-multiply and divide:
1.6 m * 0.9 m = 3.6 m * x
1.44 m² = 3.6 m * x
Divide both sides of the equation by 3.6 m:
1.44 m² / 3.6 m = x
0.4 m = x
Therefore, the height of the lamp post is 0.4 meters.