The problem asks to find the height of a tower given the angle of elevation from a point 93.2 feet away from its base. The angle of elevation is given as $38^\circ 28'$.

Solution:

1. Convert the angle to decimal form: $38^\circ 28' = 38 + \frac{28}{60} = 38.4667^\circ$

2. Apply the tangent function: In a right triangle, the tangent of the angle of elevation ($\theta$) is the ratio of the opposite side (height of the tower, $h$) to the adjacent side (distance from the point to the base, $d = 93.2$ feet): $\tan(\theta) = \frac{h}{d}$

   Solving for $h$: $h = d \cdot \tan(\theta)$

3. Substitute the values: $h = 93.2 \cdot \tan(38.4667^\circ)$

Let's compute this.The height of the tower is approximately 74.05 feet.

Would you like more details on this solution or have any other questions? Here are some related questions to explore:

1. What is the formula for finding height using sine or cosine instead of tangent?
2. How would the height change if the distance from the base is doubled?
3. How can we calculate the height of the tower using a different trigonometric function?
4. What is the significance of converting angles to decimal form?
5. How can we solve similar problems involving angles of depression?

Tip: Always make sure your calculator is set to the correct mode (degrees or radians) when performing trigonometric calculations!