an electric pole is 24 meter high casts a shadow of 20 meter long.find the height of the tree if it castes a shadow of 15 meter long under similar conditions. [explain and
make the table if direct or inverse variation]
The length of the shadow is proportional
to the height of pole (Direct variation).
h = 24/20 * 15m. =
To find the height of the tree, we can set up a proportion based on the concept of similar triangles. The height of the electric pole can be considered as the height of one triangle, and the height of the tree can be considered as the height of another triangle.
Let's define:
Height of the electric pole = H1 (given as 24 meters)
Shadow length of the electric pole = S1 (given as 20 meters)
Height of the tree = H2 (to be found)
Shadow length of the tree = S2 (given as 15 meters)
We can set up the proportion as follows:
H1 / S1 = H2 / S2
Plugging in the given values:
24 / 20 = H2 / 15
Now, let's solve for H2:
Cross multiplying, we get:
24 * 15 = H2 * 20
Simplifying:
H2 = (24 * 15) / 20
H2 = 18 meters
Therefore, the height of the tree is 18 meters.
Now, let's analyze if the relationship between height and shadow length is direct or inverse variation by creating a table.
Height (H) | Shadow Length (S)
------------------------------
24 | 20
18 | 15
In a direct variation, as one variable increases, the other variable also increases. We can see from the table that as the height decreases from 24 to 18, the shadow length also decreases from 20 to 15. This shows an inverse relationship between height and shadow length.
Therefore, the relationship between height and shadow length in this scenario is an inverse variation.