A tree casts a shadow 10 feet long. A 6-ft. man casts a shadow 4 ft. long. The triangle formed by the tree and its shadow is similar to the triangle formed by the man and his shadow. How tall is the tree?
To determine the height of the tree, we need to find the ratio of the height of the tree to the length of its shadow, and then use this ratio to find the height.
We are given that the length of the tree's shadow is 10 feet and the height of the man is 6 feet with a shadow length of 4 feet. Since the two triangles are similar, the ratio between their corresponding sides will be the same.
Let's denote the height of the tree as 'h.' According to the similarity of the triangles, the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the man to the length of his shadow. Mathematically, we can set up the following proportion:
(h / 10) = (6 / 4)
Now, we can cross-multiply and solve for 'h':
4h = 60
Dividing both sides by 4:
h = 15
Therefore, the height of the tree is 15 feet.