We can solve this problem using trigonometry. Here's how we can break it down:

Given:

• Distance from you to the building: $d = 149 \, \text{m}$
• Your eye level above the ground: $h_{\text{eye}} = 183 \, \text{cm} = 1.83 \, \text{m}$
• Angle of elevation: $\theta = 18.9^\circ$

Step 1: The height of the building

The total height of the building can be broken into two parts:

1. The height from your eyes to the top of the building, which can be found using trigonometry.
2. The height of your eyes from the ground (1.83 meters).

We need to calculate the height from your eyes to the top of the building first.

Step 2: Use the tangent function

In a right triangle, the tangent of an angle is defined as the ratio of the opposite side (height above your eyes) to the adjacent side (distance from you to the building). So,

$\tan(\theta) = \frac{\text{height above your eyes}}{\text{distance to the building}}$

$\tan(18.9^\circ) = \frac{h_{\text{top}} - h_{\text{eye}}}{d}$

Now, solving for the height above your eyes:

$h_{\text{top}} - h_{\text{eye}} = \tan(18.9^\circ) \times 149$

First, find the tangent of $18.9^\circ$:

$\tan(18.9^\circ) \approx 0.344$

Now calculate the height:

$h_{\text{top}} - h_{\text{eye}} = 0.344 \times 149 \approx 51.3 \, \text{m}$

Step 3: Add your eye height to get the total height of the building:

$h_{\text{top}} = h_{\text{eye}} + (h_{\text{top}} - h_{\text{eye}})$

$h_{\text{top}} = 1.83 + 51.3 = 53.13 \, \text{m}$

Final Answer:

The height of the building is approximately 53.13 meters.

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Would you like any further details or clarifications on this? Here are a few related questions:

1. How do we use other trigonometric functions in real-world applications like this one?
2. What happens to the height if the angle of elevation increases or decreases?
3. How would the calculation change if you were standing at a different height (e.g., on a hill)?
4. How can we apply this concept to calculate the height of other objects using angles?
5. What is the relationship between distance, angle, and height in general?

Tip: Always double-check that the angle is in the correct unit (degrees or radians) before performing trigonometric calculations.