An airplane is 50 km north and 70 km east of an airport. It is 7 km up in the air. What is the angle alon ground that the airplane is at, as a direction east of north?
a. 55.7°
c. 54.5°
b. 49.4°
d. 62.4°
To find the angle, we can use trigonometry to calculate the tangent of the angle.
Tangent = Opposite / Adjacent
In this case, the Opposite side is 70 km (east) and the Adjacent side is 50 km (north). Therefore, the tangent of the angle is:
Tangent = 70 km / 50 km = 1.4
To find the angle, we need to take the inverse tangent (arctan) of 1.4:
Angle = arctan(1.4) ≈ 54.5°
Therefore, the airplane is at an angle of approximately 54.5° east of north. The correct answer is option c. 54.5°.