From a point 50 feet in front of a church, the angle of elevation to the top of the steeple is 48 degrees. Find the overall height of the church and steeple.

tan48 = h/50,

h = 50*tan48 = 55.5ft

To find the overall height of the church and steeple, we can use the concept of trigonometry. Given that the angle of elevation to the top of the steeple is 48 degrees, we can use the tangent function to relate the angle and the height.

Let's define the overall height of the church and steeple as "h". To solve for "h", we can use the formula:

tan(angle) = opposite/adjacent.

In this case, the opposite side is the height of the church and steeple (h), and the adjacent side is the distance from the point 50 feet in front of the church to the base of the steeple.

First, let's find the adjacent side using cosine:

cos(angle) = adjacent/hypotenuse.

Since the angle is the angle of elevation and we are given the distance from the point to the church (50 feet), we can rewrite the formula as:

cos(48 degrees) = 50 feet/adjacent.

To solve for the adjacent side, we rearrange the formula as:

adjacent = 50 feet / cos(48 degrees).

Now, we have the value of the adjacent side. We can plug this value into the formula for tangent:

tan(48 degrees) = h / adjacent.

We know the value of the angle and adjacent side, so we can solve for "h":

h = tan(48 degrees) * adjacent.

By substituting the value of "adjacent" we found earlier, we can calculate the overall height of the church and steeple.