To find the height of the building, we can use trigonometric principles. Specifically, we will use the tangent function, which relates the angle of elevation to the opposite side (the height of the building) and the adjacent side (the distance from Ewa to the building).
The formula is: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case:
- \(\theta = 60^\circ\)
- The adjacent side (the distance from Ewa to the building) is 25 feet.
- The opposite side is the height of the building, which we can denote as \(h\).
Substituting these values into the tangent formula gives: \[ \tan(60^\circ) = \frac{h}{25} \]
Now, we know that \(\tan(60^\circ) = \sqrt{3}\). So, we can write:
\[ \sqrt{3} = \frac{h}{25} \]
To solve for \(h\), we multiply both sides by 25:
\[ h = 25 \cdot \sqrt{3} \]
Thus, the exact height of the building is:
\[ \boxed{25\sqrt{3}} \text{ feet} \]
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