Question

1. geometry

at a certain time of day, a flagpole casts a 9.0 - foot - long shadow and a nearby 4.0 - foot - tall fence post casts a 2.4 - foot - long shadow. given that both the flagpole and the fence post are vertical and on level ground, what is the height, in feet, of the flagpole?
f. 5.4
g. 10.6
h. 15.0
j. 15.4

1. integrating essential skills

on the real number line, how many integers are between $-\frac{65}{6}$ and $\frac{75}{2}$?

Explanation:

Step1: Set up proportion

Since the objects and their shadows form similar triangles (by the property of similar triangles in sunlight - height and shadow length are proportional), let the height of the flagpole be \(h\). We have the proportion \(\frac{\text{height of fence post}}{\text{length of fence post's shadow}}=\frac{\text{height of flagpole}}{\text{length of flagpole's shadow}}\), i.e., \(\frac{4}{2.4}=\frac{h}{9}\).

Step2: Solve for \(h\)

Cross - multiply: \(2.4h = 4\times9\). Then \(2.4h=36\). Divide both sides by \(2.4\): \(h=\frac{36}{2.4}\). Simplify \(\frac{36}{2.4}=\frac{360}{24}=15\).

Answer:

H. 15.0