A boy who is 1.8 meters tall stands 1 meter away from a lamppost and casts a shadow 2 meters long.
The height of the lamppost is
meters.
To find the height of the lamppost, we can use the concept of similar triangles.
Let h be the height of the lamppost.
According to the given information, the boy's height is 1.8 meters, and the distance between the boy and the lamppost is 1 meter. The length of the boy's shadow is 2 meters.
We can set up a proportion between the corresponding sides of the two similar triangles formed by the boy, his shadow, and the lamppost:
(Height of the boy) / (Distance between the boy and the lamppost) = (Height of the lamppost) / (Length of the lamppost's shadow)
1.8 / 1 = h / 2
Cross-multiplying the equation:
1.8 * 2 = 1 * h
3.6 = h
Therefore, the height of the lamppost is 3.6 meters.