An airplane is flying 100 km north and 185 km west of an airport. it is flying at a height of 7 km.
A) what is the straight-line distace to the airport?
B) what is the angle of elevation of the airplane, from the point of view of the airport?
5km
an airplane is flying 100km north and 185 km west
To find the straight-line distance to the airport, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance traveled north is one side of the triangle, the distance traveled west is the other side, and the straight-line distance to the airport is the hypotenuse.
Using the Pythagorean theorem, we can calculate the straight-line distance:
Distance north = 100 km
Distance west = 185 km
Straight-line distance = √(Distance north^2 + Distance west^2)
Straight-line distance = √(100^2 + 185^2)
Straight-line distance = √(10000 + 34225)
Straight-line distance = √44225
Straight-line distance ≈ 210.34 km
Therefore, the straight-line distance to the airport is approximately 210.34 km.
To find the angle of elevation of the airplane from the point of view of the airport, we can use trigonometry. Specifically, we can use the tangent function to calculate the angle.
The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the height of the plane is the side opposite the angle, and the straight-line distance to the airport is the side adjacent to the angle.
Using the tangent function, we can calculate the angle of elevation:
Height of the plane = 7 km
Straight-line distance to the airport = 210.34 km
Tangent(angle) = (Height of the plane) / (Straight-line distance to the airport)
Tangent(angle) = 7 km / 210.34 km
Tangent(angle) ≈ 0.033
To find the angle, we can take the inverse tangent (arctangent) of 0.033 using a calculator or a trigonometric table.
Angle = arctan(0.033)
Angle ≈ 1.891 degrees
Therefore, the angle of elevation of the airplane from the point of view of the airport is approximately 1.891 degrees.