Final answer:
To determine the height of the creepy old tree, we use the principle of similar triangles and set up a proportion with the monster's height and shadows. The tree height is found to be 46.8 feet tall by solving the proportion.
Step-by-step explanation:
The question presents a scenario where we need to use the principles of similar triangles to determine the height of an old tree, given that a monster's shadow and height are known, and the shadow of the tree is also known. This type of question relies on the idea that if two figures are similar, the ratios of their corresponding sides are equal.
If a monster that is 9 feet tall casts a shadow that is 5 feet long, and a creepy old tree casts a shadow that is 26 feet long, then the ratio of the tree's height to the monster's height is the same as the ratio of the tree's shadow to the monster's shadow. Therefore, we can set up a proportion to solve for the tree's height: tree height / monster height = tree shadow / monster shadow. Inputting our known values, we get the equation: tree height / 9 feet = 26 feet / 5 feet.
By solving this equation, we find that the tree height = (9 feet × 26 feet) / 5 feet, which results in a tree height of 46.8 feet. Thus, we can conclude that the creepy old tree is 46.8 feet tall.