Question

1. on a golf course, a flagstick casts a 150 - inch shadow at the same time that a nearby tee casts a 5 - inch shadow. if the tee is $2\frac{3}{4}$ inches tall, how tall is the flagstick?

Explanation:

Step1: Set up the proportion

Since the objects and their shadows form similar triangles, we can set up the proportion \(\frac{\text{height of flagstick}}{\text{length of flagstick's shadow}}=\frac{\text{height of tee}}{\text{length of tee's shadow}}\). Let \(h\) be the height of the flagstick. So, \(\frac{h}{150}=\frac{2\frac{3}{4}}{5}\).

Step2: Convert the mixed number to an improper fraction

\(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\). The proportion becomes \(\frac{h}{150}=\frac{\frac{11}{4}}{5}\).

Step3: Simplify the right - hand side of the proportion

\(\frac{\frac{11}{4}}{5}=\frac{11}{4}\times\frac{1}{5}=\frac{11}{20}\). So, \(\frac{h}{150}=\frac{11}{20}\).

Step4: Solve for \(h\)

Cross - multiply: \(20h=11\times150\). Then \(20h = 1650\). Divide both sides by 20: \(h=\frac{1650}{20}=82.5\).

Answer:

The flagstick is \(82.5\) inches tall.