Question

An airplane is flying at a height of 7 miles when it begins its descent for landing. The runway is 150 miles away from nose of the airplane along the diagonal. At what approximate angle does the airplane descend?

Answer 1

To determine the descent angle of an airplane, the height (7 miles) and the diagonal distance to the runway (150 miles) are used to calculate the angle using the inverse tangent function, resulting in an approximate angle of 2.67 degrees.

Step-by-step explanation:

Given the airplane's height of 7 miles and the diagonal distance to the runway of 150 miles, we can use trigonometry to find this angle. This situation can be represented as a right-angled triangle, where the height of the airplane is the opposite side, and the diagonal distance to the runway is the hypotenuse. To find the angle of descent, θ, we use the inverse tangent function (tan-1): θ = tan-1(opposite/hypotenuse), θ = tan-1(7 miles/150 miles), θ ≈ tan-1(0.0467), θ ≈ 2.67° (Using a calculator and rounding to two decimal places). Therefore, the airplane will commence its descent at an angle of approximately 2.67 degrees.