An airplane rises vertically 3,000 ft. over a horizontal distance of 4,500 ft. What is the angle from the ground up to the plane? Round your answer to the nearest degree.
To find the angle from the ground up to the plane, we need to use the tangent function.
The tangent of an angle θ is defined as 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 vertical distance (3,000 ft) and the side adjacent to the angle is the horizontal distance (4,500 ft).
So, the tangent of the angle is:
tan(θ) = opposite/adjacent
= 3,000/4,500
= 2/3
To find the angle, we use the inverse tangent (arctan) function. In this case:
θ = arctan(2/3)
≈ 33.69 degrees
Therefore, the angle from the ground up to the plane is approximately 34 degrees.