An aircraft takes off at an angle of 5.2degree to the ground how high is it when it has moved 2000meter horizontally from its takeoff point
make a sketch and review you basic trig definitions to see that
tan 5.2° = height/2000
solve for height
Thank you
To find the height of the aircraft, we can use trigonometry. We can assume that the horizontal distance covered is the base of a right triangle, and the height of the aircraft is the vertical side of the triangle.
Using the given information:
Angle of takeoff (θ) = 5.2 degrees
Horizontal distance (base) = 2000 meters
We can use the trigonometric function tangent to find the height:
tan(θ) = opposite / adjacent
In this case, the height is the opposite side, and the horizontal distance is the adjacent side.
tan(5.2 degrees) = height / 2000 meters
To solve for the height, we need to rearrange the equation:
height = tan(5.2 degrees) * 2000 meters
Calculating the height using this formula:
height = tan(5.2 degrees) * 2000 meters
≈ 0.0916 * 2000
≈ 183.2 meters
Therefore, the aircraft is approximately 183.2 meters high when it has moved 2000 meters horizontally from its takeoff point.
To find the height of the aircraft, we can use trigonometry. In this case, we have the horizontal distance (2000 meters) and the angle of takeoff (5.2 degrees).
We can use the tangent function, which relates the opposite side (height) to the adjacent side (horizontal distance) in a right triangle. The formula is:
tan(angle) = opposite / adjacent
Let's calculate the height:
Step 1: Convert the angle from degrees to radians.
angle_in_radians = 5.2 * (pi / 180)
Step 2: Calculate the height using the tangent function.
height = adjacent * tan(angle_in_radians)
= 2000 * tan(5.2 * (pi / 180))
Thus, the height of the aircraft when it has moved 2000 meters horizontally from its takeoff point is approximately equal to 182.1 meters.