how high is a tree that cast a 36ft shadow at the time a 12ft post cast a shadow which is 12 ft.
how high is the tree hight
x/36 = 12/12
12x = 432
x = 12
To determine the height of the tree, we can use the concept of similar triangles. Similar triangles have proportional sides.
In this case, we have two similar triangles: the first triangle consists of the tree, its shadow, and the sunlight, and the second triangle consists of the post, its shadow, and the sunlight.
Let's denote the height of the tree as h and the length of its shadow as s. Similarly, let's denote the height of the post as 12 ft and the length of its shadow as 12 ft.
Using the properties of similar triangles, we can set up the following proportion:
(post height) / (post shadow length) = (tree height) / (tree shadow length)
Substituting the given values:
12 ft / 12 ft = h / 36 ft
Now, we can solve for h by cross-multiplying and then dividing:
12 ft * 36 ft = 12 ft * h
432 ft^2 = 12 ft * h
Dividing both sides by 12 ft:
432 ft^2 / 12 ft = h
36 ft = h
Therefore, the height of the tree is 36 feet.