Question

Adrian is 1.65 meters tall. At 11 a.m., he measures the length of a tree's shadow to be 31.25 meters. He stands 27 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 setting up a proportion based on similar triangles formed by Adrian and the tree with their shadows, we solve and find that the height of the tree is approximately 12.13 meters when rounded to the nearest hundredth.

Step-by-step explanation:

The student's question is about using similar triangles to find the height of a tree. To solve this, we realize that Adrian and the tree form similar triangles with their respective shadows due to the sunlight creating corresponding angles of elevation. To solve for the height of the tree, we can use the proportion of the sides of the similar triangles.

Let's call the height of the tree H. Since the tip of Adrian's shadow meets the tip of the tree's shadow, we can set up a proportion based on the similar triangles:

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

So, 1.65 meters / 4.25 meters = H meters / 31.25 meters. By cross-multiplication, we get:

1.65 * 31.25 = 4.25 * H

H = (1.65 * 31.25) / 4.25

H = 12.13235 meters

Rounded to the nearest hundredth, the height of the tree is 12.13 meters.

Note that in the original question, the distance between Adrian and the tree (27 meters) is not relevant for calculating the height of the tree with this method since it's the lengths of the shadows and Adrian's height that are important.