Question

1. chimneys. a 6-ft observer casts a 4-ft shadow at the same time a chimney casts a 238-foot shadow. how tall is the chimney?
2. buildings the may road apartments in hong kong cast a 90-meter shadow at the same time a 1.5-meter tall tenant casts a 0.75-meter shadow. how tall is the apartment building?
3. world records the world’s tallest man lived from 1918 to 1940. he cast a 4-foot $5\frac{1}{2}$-inch shadow when a 6-foot pole cast a 3-foot shadow. how tall was he?
4. shadows a man casts a 14-foot shadow. a 4-foot child casts a 9-foot 4-inch shadow at the same time. how tall is the man?

Explanation:

Problem 7:

Step1: Set up proportion

Let $h$ = chimney height.
$\frac{h}{238} = \frac{6}{4}$

Step2: Solve for $h$

$h = 238 \times \frac{6}{4}$
$h = 238 \times 1.5 = 357$

Problem 8:

Step1: Set up proportion

Let $h$ = building height.
$\frac{h}{90} = \frac{1.5}{0.75}$

Step2: Solve for $h$

$h = 90 \times \frac{1.5}{0.75}$
$h = 90 \times 2 = 180$

Problem 9:

Step1: Convert units to inches

Pole: $6$ ft = $72$ in, pole shadow: $3$ ft = $36$ in.
Man's shadow: $4$ ft $5\frac{1}{2}$ in = $4\times12 + 5.5 = 53.5$ in.
Let $h$ = man's height (in).

Step2: Set up proportion

$\frac{h}{53.5} = \frac{72}{36}$

Step3: Solve for $h$

$h = 53.5 \times \frac{72}{36}$
$h = 53.5 \times 2 = 107$ in, convert to ft: $\frac{107}{12} = 8$ ft $11$ in

Problem 10:

Step1: Convert units to feet

Child's shadow: $9$ ft $4$ in = $9 + \frac{4}{12} = 9 + \frac{1}{3} = \frac{28}{3}$ ft.
Let $h$ = man's height.

Step2: Set up proportion

$\frac{h}{14} = \frac{4}{\frac{28}{3}}$

Step3: Solve for $h$

$h = 14 \times 4 \times \frac{3}{28}$
$h = \frac{168}{28} = 6$

Answer:

1. 357 feet
2. 190 meters
3. 8 feet 11 inches
4. 6 feet