Final answer:
To find the height of the tree, a proportion is set up using the post's known height and shadow length. Solving the equation (5 meters / 3 meters = H / 27 meters) gives the height of the tree as 45 meters.
Step-by-step explanation:
To solve the problem of finding the height of the tree, we can use similar triangles. The ratio of the height of the tree to the length of its shadow will be the same as the ratio of the height of the post to the length of its shadow.
Let's denote the height of the tree as H. We can set up the proportion as follows:
Height of post / Length of post's shadow = Height of tree / Length of tree's shadow
5 meters / 3 meters = H / 27 meters
Multiplying both sides of the equation by 27 meters to solve for H, we get:
5 meters / 3 meters * 27 meters = H
After simplifying, we find that H = (5*27)/3 = 45 meters.
Therefore, the height of the tree is 45 meters.