Final answer:
By setting up a proportion based on the relationship between Brian's height and his shadow compared to the tree's shadow, we can determine that the height of the tree is 30 feet, which is option (b).
Step-by-step explanation:
The question asks us to determine the height of a tree given that the tree casts a 20-foot shadow and comparing it to Brian who is 6 feet tall and casts a 4-foot shadow. To solve this, we can use the proportion method, where the ratio of Brian's height to his shadow is equal to the ratio of the tree's height to the tree's shadow. The equation can be set up as:
6 feet / 4 feet = tree height / 20 feet
Solving this proportion, we multiply both sides of the equation by 20 feet to get:
6 feet / 4 feet × 20 feet = tree height
Which simplifies to:
30 feet = tree height
Therefore, the height of the tree is 30 feet, which corresponds to option (b).