To find the height of the cell phone tower, we can use the tangent of the angle of elevation. The setup forms a right triangle where:
- The angle of elevation (angle from Mindy to the top of the tower) is \(75^\circ\).
- The distance from Mindy to the base of the tower (adjacent side) is \(28\) feet.
- The height of the tower (opposite side) is what we need to find.
Using the tangent function: \[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \] In our case: \[ \tan(75^\circ) = \frac{\text{height of the tower}}{28} \]
Let \(h\) be the height of the tower. We can rearrange the equation to solve for \(h\): \[ h = 28 \cdot \tan(75^\circ) \]
Now we need to calculate \(\tan(75^\circ)\): \[ \tan(75^\circ) \approx 3.732 \]
Now plug this value into the equation: \[ h \approx 28 \cdot 3.732 \] \[ h \approx 104.496 \]
Rounding to the nearest tenth: \[ h \approx 104.5 \]
Therefore, the height of the cell phone tower is approximately: \[ \text{Height of the cell phone tower} = 104.5 \text{ feet} \]
1 answer