Question
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.
The height of the lamppost is
meters.
Answers
GPT 3.5
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.
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.