A communications company erects a 100-foot tall cellular telephone tower on level ground. Determine the angle of depression, θ (in degrees), from the top of the tower to a point 43 feet from the base of the tower. Round answer to two decimal places.
I got 66.73 because tan^-1 (100/43)
To determine the angle of depression, θ, from the top of the tower to a point 43 feet from the base of the tower, we can use the tangent function.
Tan(θ) = opposite / adjacent
In this case, the opposite side is the height of the tower, which is 100 feet, and the adjacent side is the distance from the tower, which is 43 feet.
Tan(θ) = 100 / 43
Now, we can solve for θ by taking the inverse tangent (also known as arctan) of both sides:
θ = arctan(100 / 43)
Using a calculator, we find that θ is approximately 66.42 degrees (rounded to two decimal places).
Therefore, the angle of depression, θ, from the top of the tower to a point 43 feet from the base of the tower is approximately 66.42 degrees.
To determine the angle of depression, θ, from the top of the tower to a point 43 feet from the base of the tower, we can use trigonometry.
The angle of depression is the angle formed by a downward line from the top of an object to a point below it. In this case, the object is the tower, and we are interested in the angle formed between the line from the top of the tower and the line from the base of the tower to the point 43 feet away.
To find the angle of depression, we need to use the tangent function, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the side opposite the angle is the height of the tower (100 feet), and the side adjacent to the angle is the distance from the base of the tower to the point (43 feet).
Using the trigonometric identity: tangent(θ) = opposite/adjacent, we can plug in the values and solve for θ.
tangent(θ) = 100/43
To calculate θ, we need to take the inverse tangent (or arctan) of both sides of the equation:
θ = arctan(100/43)
Using a calculator, we find that arctan(100/43) ≈ 66.32 degrees.
So, the angle of depression θ, rounded to two decimal places, is approximately 66.32 degrees.