Question

Josiah is 1.35 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 18.25 meters. He stands 13.4 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

To find the height of the tree, we set up a proportion using the lengths of the shadows and distances. Solving the proportion gives us the height of the tree.

Step-by-step explanation:

To find the height of the tree, we can use similar triangles. Let's assume the height of the tree is h meters. According to the given information, the length of Josiah's shadow is 1.35 meters, the length of the tree's shadow is 18.25 meters, and the distance between Josiah and the tree is 13.4 meters.

We can set up the proportion:

(height of Josiah) / (length of Josiah's shadow) = (height of the tree) / (length of the tree's shadow)

Plugging in the values, we get:

1.35 / 13.4 = h / 18.25

Cross-multiplying and solving for h, we find that the height of the tree is approximately 1.829 meters.