The Washington monument is 555 feet high. If you are standing one quarter of a mile, or 1320 feet, from the base of the monument and looking at the top, find the angle of elevation to the nearest degree.
55/1320 = tan x
To find the angle of elevation to the top of the Washington Monument, we can use trigonometry.
Given:
Height of the monument: 555 feet
Distance from the base of the monument: 1320 feet
Let's use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Tangent of the angle of elevation = Opposite / Adjacent
In this case, the opposite side is the height of the monument (555 ft), and the adjacent side is the distance from the base of the monument (1320 ft). So, we have:
Tan(angle) = 555 / 1320
To find the angle, we can take the inverse tangent (arctan) of both sides:
Angle = arctan(555 / 1320)
Using a calculator or a math software, we can find that the arctan of 555 / 1320 is approximately 22.1 degrees.
Therefore, the angle of elevation to the top of the Washington Monument is approximately 22 degrees.
To find the angle of elevation, we can use trigonometry. We have a right triangle formed by the Washington monument, the distance from the base to the observer, and the line of sight from the observer to the top of the monument. The side opposite the angle of elevation is the height of the monument (555 feet) and the side adjacent to the angle is the horizontal distance between the observer and the monument (1320 feet).
Let's use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle. In this case, the tangent of the angle of elevation (θ) is equal to the height of the monument divided by the horizontal distance:
tan(θ) = height / distance
Plugging in the values we have:
tan(θ) = 555 / 1320
Now, to find the angle of elevation (θ), we need to calculate the inverse tangent (also known as arctan) of both sides:
θ = arctan(tan(θ))
θ = arctan(555 / 1320)
Using a calculator, we can find that:
θ ≈ 23 degrees
Therefore, the angle of elevation to the nearest degree is approximately 23 degrees.