A mini toy helicopter ascends 50 feet vertically, then flies horizontally 200 feet. Find the angle of elevation to the helicopter now as seen by an observer at the takeoff point. Round to the nearest degree
Up 50', horizontal 200' makes an angle of elevation of atan(50/200)=14° approx.
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To find the angle of elevation to the helicopter, we can use the tangent function.
Let theta represent the angle of elevation.
We are given that the helicopter ascends 50 feet vertically and flies horizontally 200 feet. This forms a right triangle.
We can use the formula:
tan(theta) = opposite/adjacent
In this case, the opposite side is the height the helicopter ascended, which is 50 feet, and the adjacent side is the horizontal distance traveled, which is 200 feet.
Therefore, tan(theta) = 50/200
Simplifying, we get:
tan(theta) = 1/4
To find theta, we can take the inverse tangent (arctan) of both sides:
theta = arctan(1/4)
Using a calculator to find the arctan of 1/4:
theta ≈ 14.04 degrees
Rounded to the nearest degree, the angle of elevation to the helicopter is approximately 14 degrees.
To find the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the helicopter.
In this case, we have a right triangle formed by the height the helicopter ascends (50 feet) and the horizontal distance it flies (200 feet). The angle of elevation is the angle opposite the height (50 feet).
To find this angle, we can use the tangent function, which is defined as the ratio of the opposite side (50 feet) to the adjacent side (200 feet):
tangent(angle) = opposite side / adjacent side
tangent(angle) = 50 feet / 200 feet
Using a calculator, we can find the angle whose tangent is equal to 0.25:
angle = arctan(0.25)
angle ≈ 14.04 degrees
Therefore, the angle of elevation to the helicopter is approximately 14 degrees.