A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft tall, how tall is the tree?
h/10 = 5/2.5
h = 20
×/10=5/4
4/4=50/4
×=12 4/54
To solve this problem, we can set up a proportion using the similar triangles.
Let's denote the height of the tree as 'h'.
According to the given information, the length of the shadow of the tree is 10 ft, and the length of the shadow of the boy is 2.5 ft. The height of the boy is known to be 5 ft.
We can set up the proportion as follows:
(height of the tree) / (length of the tree's shadow) = (height of the boy) / (length of the boy's shadow)
h / 10 = 5 / 2.5
To solve for 'h', we can cross-multiply and then divide:
2.5h = 50
h = 50 / 2.5
h = 20
Therefore, the tree is 20 ft tall.
To find the height of the tree, we can use the concept of similar triangles. Similar triangles are triangles that have the same shape but can be different in size. In this case, the triangles formed by the tree and its shadow, and the boy and his shadow are similar.
Let's assume the height of the tree is represented by 'h.'
According to the problem, the length of the tree's shadow is 10 ft, and the length of the boy's shadow is 2.5 ft. We can set up the proportion:
(Height of the tree)/(Length of the tree's shadow) = (Height of the boy)/(Length of the boy's shadow)
This can be written as:
h/10 = 5/2.5
To find the height of the tree, we'll solve for 'h.'
Cross-multiplying:
2.5h = 5 * 10
2.5h = 50
Dividing both sides by 2.5:
h = 50 / 2.5
h = 20
Therefore, the height of the tree is 20 ft.