Answer:
C. 58.9 meters
Explanation:
To find the height of the tower, we can use trigonometry. In this case, we have a right triangle formed by the surveyor, the top of the tower, and the base of the tower. The angle between the surveyor and the top of the tower is 61.8°, and the distance between the surveyor and the base of the tower is 75 meters.
To find the height of the tower, we need to determine the length of the side opposite the angle (which represents the height of the tower) in the right triangle. We can use the trigonometric function tangent (tan) to solve for the height.
Step 1: Identify the relevant trigonometric function:
In this case, we'll use the tangent function because we know the angle and the length of the adjacent side.
Step 2: Apply the trigonometric function:
The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side. Therefore, we can use the formula:
tan(angle) = opposite/adjacent
In this case, the angle is 61.8°, and the adjacent side is 75 meters. Let's call the height of the tower "h".
So, we have:
tan(61.8°) = h/75
Step 3: Solve for the height of the tower:
To find the value of "h", we can rearrange the equation:
h = tan(61.8°) * 75
Using a calculator, we find:
h ≈ 58.9 meters
Therefore, the height of the tower is approximately 58.9 meters.
So, the correct answer is c) 58.9 meters.