Question

Camden is 1.35 meters tall. At 12 noon, he measures the length of a tree's shadow to be 19.35 meters. He stands 14.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer 1

By using the similarity of triangles method, the height of the tree is calculated as approximately 1.82 meters tall, rounded to the nearest hundredth of a meter.

Step-by-step explanation:

To find the height of the tree, we can use the similarity of triangles method. Since the tips of the shadows of the tree and Camden meet, and both the tree and Camden are standing upright, we have two similar right-angled triangles:

• Triangle 1: The tree and its shadow
• Triangle 2: Camden and his shadow

The corresponding sides of similar triangles are in the same ratio, so the ratio of Camden's height to the length of his shadow is equal to the ratio of the tree's height to the length of its shadow. Therefore, we can express this as:

Camden's height / Camden's shadow length = Tree's height / Tree's shadow length

1.35 m / 14.2 m = Tree's height / 19.35 m

We can now solve for the tree's height:

Tree's height = (1.35 m / 14.2 m) * 19.35 m

Tree's height ≈ 1.8246478873239436 m

Rounding to the nearest hundredth of a meter, we find the tree is approximately 1.82 meters tall.