To solve for the height of the building, we can use trigonometric relationships in a right triangle formed by the height of the building, the length of the shadow, and the line from the top of the building to the end of the shadow.
Here, we have:
- The length of the shadow = 150 meters
- The angle at the end of the shadow = 45 degrees
Using the tangent function, which is defined as the ratio of the opposite side (the height of the building) to the adjacent side (the length of the shadow):
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case:
\[ \tan(45^\circ) = \frac{\text{height}}{150} \]
Since \(\tan(45^\circ) = 1\), the equation simplifies to:
\[ 1 = \frac{\text{height}}{150} \]
To find the height, we multiply both sides by 150:
\[ \text{height} = 150 \text{ m} \]
Thus, the height of the building is 150 meters.
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