To solve this problem, we can use the concept of similar triangles. The tower and the post cast shadows at the same time, which means the angle of elevation of the sun is the same for both, creating two similar triangles. Let's denote the height of the tower as $ h $ and the length of its shadow as 114 ft. We are given that a 9.0-ft post casts an 8.0-ft long shadow. We can set up a proportion using the corresponding sides of the similar triangles: \[ \frac{\text{Height of post}}{\text{Length of post's shadow}} = \frac{\text{Height of tower}}{\text{Length of tower's shadow}} \] Substituting the given values: \[ \frac{9.0}{8.0} = \frac{h}{114} \] Now we can solve for $ h $: \[ h = \frac{9.0}{8.0} \times 114\] \[ h = 1.125 \times 114\] \[ h = 128.25 \text{ ft} \] Rounding to the nearest unit, the height of the tower is approximately 128 feet.

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To solve this problem, we can use the concept of similar triangles. The tower and the post cast shadows at the same time, which means the angle of elevation of the sun is the same for both, creating two similar triangles. Let's denote the height of the tower as $h$ and the length of its shadow as 114 ft. We are given that a 9.0-ft post casts an 8.0-ft long shadow. We can set up a proportion using the corresponding sides of the similar triangles: $\frac{\text{Height of post}}{\text{Length of post's shadow}} = \frac{\text{Height of tower}}{\text{Length of tower's shadow}}$ Substituting the given values: $\frac{9.0}{8.0} = \frac{h}{114}$ Now we can solve for $h$ : $h = \frac{9.0}{8.0} \times 114$ $h = 1.125 \times 114$ $h = 128.25 \text{ ft}$ Rounding to the nearest unit, the height of the tower is approximately 128 feet.

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