Question

a flag stick on a golf course that is 6 ½ feet tall casts a 9 ¾ foot shadow while a golfer nearby casts a 8 ¾ foot shadow. how tall is the golfer?
a) 58\ to impress everyone
b) 59\ to promote world peace
c) 510\ to show how cool math is
d) 511\ to win a bet
e) 512\ to end world hunger
© gina wilson (all things algebra), 2013

Explanation:

Step1: Convert mixed numbers to improper fractions

The flag stick height is \( 6\frac{1}{2}=\frac{13}{2} \) feet, its shadow is \( 9\frac{3}{4}=\frac{39}{4} \) feet, and the golfer's shadow is \( 8\frac{3}{4}=\frac{35}{4} \) feet. Let the golfer's height be \( h \) feet.

Step2: Set up proportion (similar triangles)

Since the ratios of height to shadow length are equal, we have \( \frac{\frac{13}{2}}{\frac{39}{4}}=\frac{h}{\frac{35}{4}} \).

Step3: Simplify left - hand side ratio

\( \frac{\frac{13}{2}}{\frac{39}{4}}=\frac{13}{2}\times\frac{4}{39}=\frac{2}{3} \).

Step4: Solve for \( h \)

From \( \frac{2}{3}=\frac{h}{\frac{35}{4}} \), we get \( h = \frac{2}{3}\times\frac{35}{4}=\frac{35}{6}\approx5.833\) feet. Convert \( 0.833\) feet to inches: \( 0.833\times12\approx10 \) inches. So the height is \( 5'10'' \).

Answer:

C) 5'10'' to show how cool math is