What angle east of north should the airplane head in order to reach its destination in a straight flight?
The airplane should head at approximately 63 degrees, east of north, to reach its destination in a straight path. This is determined using basic trigonometry principles.
Trigonometry in Action
Trigonometry plays a crucial role in determining the angle at which the airplane should head to reach its destination after traveling both northward and eastward. In this scenario, we can visualize the airplane's displacement as forming a right triangle, with the northward distance as the adjacent side and the eastward distance as the opposite side. By applying the tangent function, we can calculate the angle east of north that the airplane should head.
To answer the student's question, the airplane needs to navigate in a way that incorporates both its northward and eastward travels. We can use the concept of trigonometry to solve this problem, specifically the tangent of the angle. The tangent of an angle in a right triangle is defined as the length of the opposite side over the length of the adjacent side. Here, the northward distance comprises the 'adjacent' side (100 km), and the eastward distance is the 'opposite' side (200km). So if we denote the angle the airplane should head as θ, we have tan(θ) = 200/100. This means θ = arctan(2).
When we calculate arctan(2) in degrees we get approximately 63 degrees. So, the airplane should head at 63 degrees east of north for a straight flight to its destination.
Concluding the Angle
The closest value is (c) 63 degrees. This angle of flight represents the direction east of north that the airplane should head in order to reach its destination in a straight flight after traveling 100 km north and 200 km east. The airplane's displacement forms a right triangle with the north and east directions as its legs. The angle east of north can be found using trigonometric ratios. The tangent of the angle is the ratio of the length of the eastward displacement to the length of the northward displacement.
Tangent(angle) = East Displacement / North Displacement
Tangent(angle) = 200 km / 100 km
Tangent(angle) = 2
To find the angle itself, take the arctangent (inverse tangent) of 2:
Angle = arctan(2)
Therefore, the airplane should head at approximately 63 degrees east of north to ensure a straight flight path to its destination.