Final answer:
The height of a tree with a shadow of 20.3 feet, when another tree 5.1 feet tall casts a 6.8 feet shadow at the same time of day, is approximately 15.22 feet. This calculation is based on the concept of similar triangles and proportional reasoning.
Step-by-step explanation:
The question is about finding the height of a tree based on the height and shadow length of another tree. To solve this problem, we can use the concept of similar triangles. If Tree A is 5.1 feet tall and casts a shadow of 6.8 feet, and Tree B casts a shadow of 20.3 feet at the same time of day, we can set up a proportion because the sun's angle is the same for both shadows:
(Height of Tree A) / (Shadow of Tree A) = (Height of Tree B) / (Shadow of Tree B)
Substituting the known values, we get:
5.1 ft / 6.8 ft = (Height of Tree B) / 20.3 ft
Cross-multiplying to solve for the height of Tree B:
(5.1 ft × 20.3 ft) / 6.8 ft = Height of Tree B
Calculate the value:
(103.53 ft²) / 6.8 ft = 15.22 ft (approximately)
So, the tree with a shadow of 20.3 feet is approximately 15.22 feet tall.