Question

Noah is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.2 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

To find the height of the tree, establish a proportion using the lengths of Noah's shadow and his own height compared to the distance between him and the tree.

Step-by-step explanation:

To find the height of the tree, we can use similar triangles.

The height of Noah is 1.35 meters and the length of his shadow is 31.55 meters.

The distance between Noah and the tree is 26.2 meters. Let's call the height of the tree h meters.

Using the properties of similar triangles, we can set up the following proportion:

(h / 31.55) = (1.35 / 26.2)

Cross-multiplying, we get:

h = (31.55 * 1.35) / 26.2

Calculating this, we find that the height of the tree is approximately 1.63 meters.