Answer: Let's call the height of the steeple "h". We can use the tangent function to set up an equation involving the angles of elevation:
tan(40°) = h / x
tan(49° 40') = (h + y) / x
where "x" is the distance from the point to the base of the steeple, and "y" is the height of the point above the ground.
We are given that the distance from the point to the church is 48 feet, so we can use the Pythagorean theorem to find the value of "y":
y^2 = x^2 - 48^2
We can substitute this expression for "y" into the second equation above:
tan(49° 40') = (h + √(x^2 - 48^2)) / x
We can now solve this equation for "h":
h = x tan(49° 40') - x √(1 + tan^2(49° 40')) + 48 tan(40°)
Plugging in the values for the angles and solving for "h", we get:
h ≈ 83.9 feet
Therefore, the height of the steeple is approximately 83.9 feet.
Explanation: