Question

Connor is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be 21.65 meters. He stands 17.3 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

The height of the tree is calculated using similar triangles formed by Connor's height and shadow and the tree and its shadow. By setting up a proportion and solving for the unknown tree height, we determine that the tree is approximately 2.20 meters tall.

Step-by-step explanation:

To find the height of the tree using the shadow length, we can apply similar triangles methodology because the sun's rays are parallel, creating similar triangles between Connor's height and shadow and the tree's height and shadow.

First, we set up a proportion with the known values: Connor's height (1.75 meters) and the length of his shadow (17.3 meters), and the unknown tree height and the measured tree shadow (21.65 meters).

The proportion looks like this:

• Connor's height / Connor's shadow = Tree's height / Tree's shadow
• 1.75 m / 17.3 m = Tree height / 21.65 m

Then we cross-multiply and solve for the tree's height:

1.75 m * 21.65 m = Tree height * 17.3 m

Tree height = (1.75 m * 21.65 m) / 17.3 m

Calculating yields the tree height:

Tree height = 2.20 meters (to the nearest hundredth)

Therefore, the height of the tree is approximately 2.20 meters.