Question

carl is 5 feet tall and casts a 7-foot shadow. At the same time, a tree casts a 14-foot shadow. The triangles formed are similar. Find the height of the tree.

Answer 1

The height of the tree is found using similar triangles. Carl and the tree cast shadows at ratios proportional to their heights. By solving the proportion 5/7 = x/14, we find that the tree's height is 10 feet.

Step-by-step explanation:

To find the height of the tree, we can use the properties of similar triangles. Since Carl is 5 feet tall and casts a 7-foot shadow, and the tree casts a 14-foot shadow, the ratio of Carl's height to his shadow is 5/7. This ratio should be the same for the tree because the triangles are similar.

Let x be the height of the tree. Then, the ratio of the tree's height to its shadow is x/14.

Therefore, we have the proportion:

• Carl's height/shadow = Tree's height/shadow
• 5/7 = x/14

To find the value of x, cross-multiply and solve for x:

• (5)(14) = (7)(x)
• 70 = 7x
• x = 70/7
• x = 10

So, the height of the tree is 10 feet.