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 can use the tangent function in trigonometry. The tangent of an angle 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 problem, the side opposite the angle would be the vertical distance the airplane rises, which is 3,000 ft, and the side adjacent to the angle would be the horizontal distance, which is 4,500 ft.
Therefore, the tangent of the angle is given by:
tangent(angle) = opposite/adjacent = 3,000/4,500 = 2/3
To find the angle, we can take the inverse tangent (also known as arctan or tan^(-1)) of the ratio. Using a calculator, the inverse tangent of 2/3 is approximately 33.69 degrees.
Therefore, the angle from the ground up to the plane is approximately 33.69 degrees. Rounding to the nearest degree, the answer is 34 degrees.