To find the height of the cell phone tower, we can use the tangent function, which relates the angle of elevation, the height of the opposite side (the tower), and the distance from the observer (Mindy) to the base of the tower (the adjacent side).
Given:
- Angle of elevation (\(\theta\)) = 75 degrees
- Distance from Mindy to the base of the tower (adjacent side) = 28 feet
We can use the tangent function defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Let \(h\) be the height of the tower (the opposite side). Thus, we have:
\[ \tan(75^\circ) = \frac{h}{28} \]
To find \(h\), we can rearrange the equation:
\[ h = 28 \cdot \tan(75^\circ) \]
Now we calculate \(\tan(75^\circ)\):
\[ \tan(75^\circ) \approx 3.7321 \]
Now substituting this value into the equation for \(h\):
\[ h = 28 \cdot 3.7321 \approx 104.497 \]
Rounding to the nearest tenth, we get:
\[ h \approx 104.5 \text{ feet} \]
Thus, the height of the cell phone tower is approximately 104.5 feet.