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Answer :
The nearby tower is approximately 73 meters tall, determined using the concept of similar triangles and the given measurements of the pole and its shadow, along with the tower's shadow.
We can use the concept of similar triangles to solve this problem.
The ratio of the height of the pole to its shadow length will be the same as the ratio of the height of the tower to its shadow length, since the angles of elevation of the sunlight are the same for both objects.
Let h be the height of the tower.
Using the ratios:
[tex]\[ \frac{3.2}{1.69} = \frac{h}{38.5} \][/tex]
We can solve for h:
[tex]\[ h = \frac{3.2 \times 38.5}{1.69} \][/tex]
[tex]\[ h \approx \frac{123.2}{1.69} \][/tex]
[tex]\[ h \approx 72.83 \][/tex]
Rounding to the nearest meter, the height of the tower is approximately 73 meters.
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