The height of the tree is approximately 2.4 meters, to the nearest hundredth of a meter.
1. Set up the proportion:
The height of the tree is proportional to the length of its shadow, and Cameron's height is proportional to the length of his shadow. We can write this as a proportion:
Height of tree / Length of tree shadow = Cameron's height / Length of Cameron's shadow
2. Substitute the known values:
Height of tree: Unknown (let's call it h)
Length of tree shadow: 21.55 meters
Cameron's height: 1.85 meters
Length of Cameron's shadow: 16.6 meters
Substituting these values into the proportion, we get:
h / 21.55 = 1.85 / 16.6
3. Solve for h:
Multiply both sides of the equation by 21.55:
h = (1.85 meters)(21.55 meters) / 16.6 meters
h ≈ 2.43 meters
4. Round the answer:
Round the answer to the nearest hundredth of a meter:
h ≈ 2.43 meters (rounded to two decimal places)
Therefore, the height of the tree is approximately 2.43 meters.