What would be the angle of elevation to the top of a radio transmitting tower 100 metre tall and 400 from the observer?
To calculate the angle of elevation to the top of the radio transmitting tower, you can use trigonometry. In this case, we will use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Step 1: Identify the values given in the problem:
- Opposite side (O): The height of the radio transmitting tower = 100 meters
- Adjacent side (A): The distance from the observer to the tower = 400 meters
Step 2: Use the tangent function to calculate the angle of elevation (θ):
- tan(θ) = O / A
Step 3: Solve for θ:
- θ = arctan(O / A)
Plugging in the values:
- θ = arctan(100 / 400)
Step 4: Calculate the angle of elevation using a scientific calculator or a trigonometric table:
- θ ≈ 14.04 degrees
Therefore, the angle of elevation to the top of the radio transmitting tower is approximately 14.04 degrees.