The length of the shadow of a tree. 20m is 2013 m. What will be the shadow of the pole 16√3mh high at the same time? Find it
To find the shadow of the pole, we need to determine the proportion between the height of the pole and the length of its shadow.
Let's set up a proportion:
Height of pole / Length of shadow = Height of tree / Length of shadow of the tree
Plugging in the values we have:
(16√3) / Length of shadow = 20 / 2013
Cross-multiplying, we get:
(16√3) * 2013 = 20 * Length of shadow
Simplifying, we have:
(16√3) * 2013 = 20 * Length of shadow
Multiply 16 and 2013:
32208√3 = 20 * Length of shadow
Divide both sides by 20:
(32208√3)/20 = Length of shadow
Simplifying:
1610.4√3 = Length of shadow
Therefore, the shadow of the pole at the same time will be approximately 1610.4√3 meters long.
To find the length of the shadow of the pole, we can use the concept of similar triangles.
Let's assume that the height of the tree is 'h' and the length of its shadow is 's'. We are given that the length of the tree's shadow (s) is 2013 m when the height of the tree (h) is 20 m.
Using the concept of proportions, we can set up the following equation:
s/h = 2013/20
Now, let's find the value of 's' when the height of the pole is 16√3 m.
s/16√3 = 2013/20
To find 's', we can cross-multiply:
s = (16√3 * 2013) / 20
Simplifying further:
s = (16 * √3 * 2013) / 20
Now, let's calculate the value of 's':
s ≈ 241.95 m
Therefore, the length of the shadow of the pole, when the height of the pole is 16√3 m, will be approximately 241.95 m at the same time.
To find the length of the shadow of the 16√3 m high pole at the same time, we can use the concept of similar triangles.
Let's assume that the length of the shadow of the pole is x. We can set up a proportion with the similar triangles formed by the tree, its shadow, the pole, and its shadow.
The height of the tree is 20 m, and the length of its shadow is 2013 m. The height of the pole is 16√3 m, and we are trying to find the length of its shadow, x.
We can set up the proportion as follows:
(height of tree)/(length of tree shadow) = (height of pole)/(length of pole shadow)
20/2013 = (16√3)/x
To solve for x, we can cross-multiply and then divide:
20 * x = (2013 * 16√3)
x = (2013 * 16√3) / 20
Simplifying, we have:
x = 32208√3 / 20
To further simplify, we can divide both the numerator and denominator by 4:
x = 8052√3 / 5
Therefore, the length of the shadow of the 16√3 m high pole at the same time will be 8052√3 / 5 m.