After flying at an altitude of 9 kilometers, an airplane starts to descend when its ground distance from the landing field is 175 kilometers. To the nearest degree what is the angle of depression for this portion of the flight?
tan theta = 9/175
tan-1(9/175)=2.944
Angle of Depression is 3 Degrees
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle between the line of sight from the airplane to the landing field and the horizontal line.
In this scenario, we have a right triangle formed by the plane, the landing field, and a point directly below the airplane on the ground.
Let's label the sides of the right triangle:
- The opposite side is the altitude, which is 9 kilometers.
- The adjacent side is the horizontal distance, which is 175 kilometers.
The angle of depression can be determined using the tangent function:
tan(angle) = opposite/adjacent
tan(angle) = 9/175
To find the angle, we need to take the inverse tangent (arctan) of the result:
angle = arctan(9/175)
Using a calculator, we can approximate the angle:
angle ≈ 2.94 degrees (nearest degree)
Therefore, the angle of depression for this portion of the flight is approximately 2.94 degrees.
To find the angle of depression, we need to visualize the situation. The angle of depression is the angle formed between a horizontal line and the line of sight from an observer looking downward to a point below the horizontal line.
In this case, the horizontal line represents the ground distance from the landing field, which is 175 kilometers. The line of sight is a straight line connecting the airplane and the landing field. We know that the airplane is flying at an altitude of 9 kilometers, so the line of sight is slanting downward from the airplane to the landing field.
To find the angle of depression, we can use trigonometry. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the change in altitude (9 kilometers) and the adjacent side is the ground distance (175 kilometers).
Therefore, we can use the formula: tangent(angle) = opposite/adjacent.
tangent(angle) = 9/175.
Now, we need to find the angle. We can take the inverse tangent (also known as arctan or tan^(-1)) of both sides to isolate the angle.
angle = tan^(-1)(9/175).
Calculating this value using a calculator, we find that the angle of depression is approximately 2.93736 degrees. Rounded to the nearest degree, the angle of depression for this portion of the flight is approximately 3 degrees.