At a certain time of day, a pole, 5 meters tall, casts a 3 meter shadow.
OK. That is not very interesting.
To find the height of the pole, we can use the concept of similar triangles. Let's consider the triangle formed by the pole, its shadow, and the sunlight. We can label the height of the pole as 'h' and the length of its shadow as 's'.
By observing similar triangles, we know that the corresponding sides are proportional. This means that the ratio of the height of the pole to the length of its shadow will be the same as the ratio of the height of any other object to its shadow in the same lighting conditions.
Using this information, we can set up the following proportion:
h/s = 5/3
Now, to solve for the height of the pole:
h = (5/3) * s
Given that the length of the shadow is 3 meters:
h = (5/3) * 3
Simplifying, we have:
h = 5 meters
Therefore, the height of the pole is 5 meters.