The tallest television transmitting tower in the world is in North Dakota, and it is 2059 feet tall. If you are on level ground exactly 5280 feet (one mile) from the base of the tower, what is your angle of elevation looking up at the top of the tower?
tanØ = 2059/5280 = ...
Ø = 21.3°
dew
t4g5
To find the angle of elevation, we can use basic trigonometry. We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the height of the tower is the opposite side, and the distance from the base of the tower to the observer is the adjacent side. So, we have:
Opposite side = height of the tower = 2059 feet
Adjacent side = distance from the base of the tower = 5280 feet
Using the tangent function, we can calculate the angle of elevation (θ) as:
tan(θ) = opposite side / adjacent side
tan(θ) = 2059 / 5280
To find the value of θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(2059 / 5280)
Now, let's solve this using a calculator or a math software:
θ ≈ 22.5 degrees
Therefore, the angle of elevation looking up at the top of the tower from a distance of one mile is approximately 22.5 degrees.