To find the height of the building, we can use some basic trigonometry. We know the length of the shadow and the angle at which the shadow meets the line from the tip of the building to the end of the shadow.
Let:
- \( h \) be the height of the building.
- The length of the shadow is \( 100 \) meters.
- The angle between the shadow and the line from the top of the building to the end of the shadow is \( 45^\circ \).
Using the tangent function, we have:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, the opposite side is the height of the building (\( h \)), and the adjacent side is the length of the shadow (100 meters). Since \( \theta = 45^\circ \):
\[ \tan(45^\circ) = 1 \]
Therefore,
\[ \frac{h}{100} = 1 \]
Solving for \( h \):
\[ h = 100 \text{ m} \]
Thus, the height of the building is 100 meters.
1 answer