Answer:
12 feet
Explanation:
To solve this problem, we can use the concept of similar triangles. Let's assume that Tyler's height and his shadow form one triangle, and the height of the tree and its shadow form another triangle. Since the angles in both triangles are assumed to be the same, the triangles are similar.
We are given that Tyler's height is 6 feet and his shadow is 10 ½ feet long. Maddie measures the shadow of the tree to be 21 feet long. Let's denote the height of the tree as 'h.'
Using the concept of similar triangles, we can set up a proportion:
(height of Tyler) / (length of Tyler's shadow) = (height of the tree) / (length of the tree's shadow)
6 / 10.5 = h / 21
To solve for 'h,' we can cross-multiply:
6 * 21 = 10.5 * h
126 = 10.5h
To find the value of 'h,' we divide both sides of the equation by 10.5:
h = 126 / 10.5
h ≈ 12
Therefore, the height of the tree is approximately 12 feet.
Hope this helps!