An airplane is 35 km north and 55 km east of an airport. It is 8 km up in the air. What is the angle of elevation of the airplane, from the point of view of the airport?
7.0°
7.2°
7.9°
6.9°
To find the angle of elevation of the airplane, we can consider the airplane, the airport, and the point of view of the airport as forming a right triangle. The side opposite to the angle of elevation is the vertical distance from the airplane to the airport (8 km), and the side adjacent to the angle of elevation is the horizontal distance from the airplane to the airport (55 km). Using the tangent function, we can find the angle of elevation:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = 8/55
Now, we can take the inverse tangent of both sides to find the angle of elevation:
angle of elevation = arctan(8/55)
angle of elevation ≈ 7.143°
Rounded to one decimal place, the angle of elevation of the airplane from the point of view of the airport is approximately 7.1°. None of the given answer choices match this result exactly, so the closest option is 7.0°.