Final answer:
To determine the height of the flagpole, we rely on the properties of similar triangles formed by the objects and their shadows. Using the given dimensions of a streetlight's height and shadow and the flagpole's shadow, we found that the height of the flagpole is 30 feet.
Step-by-step explanation:
To find the height of the flagpole, we can use proportions since the streetlight and the flagpole are both casting shadows due to the same light source. This creates two similar triangles, one with the streetlight and its shadow and the other with the flagpole and its shadow.
Let h be the height of the flagpole. According to the problem, a streetlight that is 10 feet tall casts a 2.5-foot-long shadow. A nearby flagpole casts a 7.5-foot-long shadow. Setting up a proportion based on similar triangles, we have:
Streetlight height / Streetlight shadow = Flagpole height / Flagpole shadow
10 feet / 2.5 feet = h / 7.5 feet
Multiplying both sides by 7.5 feet to solve for h, we get:
h = (10 feet × 7.5 feet) / 2.5 feet
h = 30 feet
Therefore, the height of the flagpole is 30 feet.