Question

A flagpole casts a shadow that is 14 feet long. At the same time, a person standing nearby who is 5 feet 6 inches tall casts a shadow

that is 42 inches long. How tall is the flagpole?
Flagpole:
feet

Answer 1

22 feet

Explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

• 14 ft = 14 × 12 = 168 inches
• 5 ft 6 in = 5 × 12 + 6 = 66 inches

Therefore:

• Flaghole height = h in
• Flagpole shadow = 168 in
• Person height = 66 in
• Person shadow = 42 in

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel. Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

`\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow`

`\implies \sf h:168=66:42`

`\implies \sf (h)/(168)=(66)/(42)`

`\implies \sf h=(66)/(42) \cdot 168`

`\implies \sf h=(11088)/(42)`

`\implies \sf h=264\;inches`

Convert the height into feet by dividing by 12:

`\implies \sf h=(264)/(12)=22\;feet`

Therefore, the height of the flagpole is 22 feet.