To determine which building is taller, we'll use the tangent function from trigonometry, which relates the angle of elevation to the height of the building and the distance from it.
The formula for the height \( h \) of a building based on the angle of elevation \( \theta \) and the distance \( d \) from the building is:
\[ h = d \cdot \tan(\theta) \]
For Building A:
- Distance \( d_A = 40 \) feet
- Angle of elevation \( \theta = 59^\circ \)
Calculating the height \( h_A \):
\[ h_A = 40 \cdot \tan(59^\circ) \]
Using a calculator, we find that:
\[ \tan(59^\circ) \approx 1.6643 \]
So,
\[ h_A = 40 \cdot 1.6643 \approx 66.57 \text{ feet} \]
For Building B:
- Distance \( d_B = 60 \) feet
- Angle of elevation \( \theta = 59^\circ \)
Calculating the height \( h_B \):
\[ h_B = 60 \cdot \tan(59^\circ) \]
Using the same value for \( \tan(59^\circ) \):
\[ h_B = 60 \cdot 1.6643 \approx 99.86 \text{ feet} \]
Comparing Heights:
- Height of Building A: \( h_A \approx 66.57 \) feet
- Height of Building B: \( h_B \approx 99.86 \) feet
Conclusion:
Now we compare the heights to determine which building is taller and by how much:
\[ h_B - h_A \approx 99.86 - 66.57 \approx 33.29 \text{ feet} \]
Therefore, Building B is approximately 33.29 feet taller than Building A.
The correct answer is: Building B; it is around 33.29 feet taller than building A.
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