Question

Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters. She stands 23.1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. -28.15 m (Diagram is not to scale.) T 1.85 m 23.1 m-​

Answer 1

To find the height of the tree, set up a proportion using the similar triangles formed by Kayla and the tree. The height of the tree is approximately [height].

Step-by-step explanation:

To find the height of the tree, we can set up a proportion using the similar triangles formed by Kayla and the tree. Let's call the height of the tree T.

According to the problem statement, Kayla's height (1.85 meters) is the height of her shadow (28.15 meters) and the distance between her and the tree (23.1 meters) is the same as the length of the tree's shadow.

We can write the following proportion: h/T = x/L, where h is Kayla's height, T is the height of the tree, x is the length of Kayla's shadow (28.15 meters), and L is the length of the tree's shadow (23.1 meters).

Substituting the given values, we get: 1.85/T = 28.15/23.1.

Cross-multiplying and solving for T gives us the height of the tree to the nearest hundredth of a meter.