How high is a tree that casts a 34ft shadow at the same time a 7 ft pole cast a shadow which is 9ft long. What is the tree's hight
7/9 = x/34
Cross multiply and solve for x.
To find the height of the tree, we can use the property of similar triangles and set up a proportion. The proportion will be between the height of the tree and the length of its shadow compared to the height of the pole and the length of its shadow.
Let's label the height of the tree as 'H' and the length of its shadow as 'S'. We can also label the height of the pole as 'P' and the length of its shadow as 'p'.
Based on the information given, we have:
Shadow of the tree (S) = 34 ft
Height of the pole (P) = 7 ft
Shadow of the pole (p) = 9 ft
The proportion can be set up as follows:
(S / H) = (p / P)
Substituting the given values:
(34 / H) = (9 / 7)
To solve for H, cross-multiply and solve for H:
34 * 7 = 9 * H
238 = 9H
Divide both sides by 9:
238 / 9 = H
H ≈ 26.44
Therefore, the height of the tree is approximately 26.44 feet.
To determine the tree's height, we need to use the concept of similar triangles.
Let's first define the variables:
Let h be the height of the tree.
Let s be the length of the tree's shadow.
According to the problem, the height of the pole is 7ft, and its shadow is 9ft long.
Using the concept of similar triangles, we can set up the following proportion:
Height of tree / Length of tree's shadow = Height of pole / Length of pole's shadow
h / s = 7 / 9
Now, we can rearrange the equation to solve for the height of the tree:
h = (s * 7) / 9
Since the tree's shadow is given as 34ft, we can substitute this value into the equation:
h = (34 * 7) / 9
Calculating this equation, we find:
h = 238 / 9
h ≈ 26.44 ft
Therefore, the height of the tree is approximately 26.44 feet.