Final answer:
To determine the height of the tower, we use the tangent function with the angle of elevation of 32 degrees and the distance of 100 feet. The calculation reveals that the tower is approximately 62 feet tall, rounded to the nearest foot.
Step-by-step explanation:
To find the height of the tower in the question, we can use trigonometry. We have an angle of elevation to the top of the tower of 32 degrees from a point 100 feet away from the base of the tower. The tower, the point on the ground, and the base of the tower form a right-angled triangle. We can use the tangent function, which relates the angle of elevation to the ratio of the opposite side (the height of the tower) over the adjacent side (the distance from the point to the base of the tower).
The tangent of the angle of elevation (32 degrees) is equal to the opposite side (height of the tower) divided by the adjacent side (100 feet).
tan(32°) = height / 100 feet
By rearranging the equation and solving for the height, we get:
height = 100 feet * tan(32°)
Using a calculator, we find tan(32°) ≈ 0.6249.
Therefore, the height of the tower is approximately:
height ≈ 100 feet * 0.6249 ≈ 62.49 feet
To the nearest foot, the tower is 62 feet tall.