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Answer:
The height of flagpole to the nearest foot is 58 feet.
Step-by-step explanation:
Given information:
Shadow of flagpole = 40 feet
Height of man = 6 feet
Shadow of man = 50 inches
We know that 1 feet = 12 inches
50 inches = [tex]\frac{50}{12}[/tex] feet
The actual height and shadow of man and flagpole are proportional.
Let the height of flagpole is h.
For flagpole,
[tex]\frac{height}{shadow}=\frac{h}{40}[/tex]
For man,
[tex]\frac{height}{shadow}=\frac{6}{\frac{50}{12}}\Rightarrow \frac{72}{50}=1.44[/tex]
Since the height and shadow of man and flagpole are proportional.
[tex]\frac{h}{40}=1.44[/tex]
Multiply both sides by 40.
[tex]h=1.44\times 40[/tex]
[tex]h=57.6\approx 58[/tex]
Therefore the height of flagpole to the nearest foot is 58 feet.
The height of the flagpole to the nearest feet is 58 feet
Similar triangle
Similar triangle are not necessarily the same sizes. There corresponding angles are congruent. The corresponding sides are ratio of each other.
The flag post triangle form a similar triangle with the man standing nearby.
Therefore, let's establish the following proportion to find the height of the flagpole.
50 inches = 4.16667 ft
- x / 40 = 6 / 4.16667
cross multiply
4.16667x = 240
x = 240 / 4.16667
x = 57.59995392
x = 58 feet.
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