An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. To the nearest degree what is the angle of elevation of the airplane’s path?
what is arctan(1000/5280) ?
To find the angle of elevation of the airplane's path, we can use trigonometry. In this case, we have a right triangle formed by the horizontal distance traveled by the airplane, the vertical distance it rises, and the hypotenuse (path of the airplane). The angle of elevation is the angle between the horizontal and the hypotenuse.
To begin, we can convert the horizontal distance of 1 mile and the vertical distance of 1000 feet into a consistent unit. Since 1 mile is equal to 5280 feet, the horizontal distance is 5280 feet.
Now, we can use the tangent function (tan) to find the angle of elevation. The tangent of an angle is the ratio of the opposite side (the vertical distance) to the adjacent side (the horizontal distance).
tan(angle) = (opposite side) / (adjacent side)
Let's substitute the values:
tan(angle) = 1000 feet / 5280 feet
Calculating this using a calculator, we find:
tan(angle) ≈ 0.1894
Now, to find the angle itself, we can use the inverse tangent function (arctan or tan^(-1)).
angle ≈ arctan(0.1894)
Calculating this using a calculator or trigonometric tables, we find:
angle ≈ 10.86 degrees
Therefore, to the nearest degree, the angle of elevation of the airplane's path is approximately 11 degrees.