An airplane is 35 km north and 55 km east of an airport. It is 7 km up in the air. What is the angle along the ground that the airplane is at, as a direction east of north?
To find the angle along the ground that the airplane is at, we can use the tangent function.
Let's consider the right triangle formed by the airplane's position, the airport, and the point directly below the airplane on the ground.
The distance along the ground from the airplane to the point directly below it is 55 km (east). The distance vertically from the airplane to the point directly below it is 7 km (up).
Using the tangent function, we can calculate the angle as follows:
tangent(angle) = opposite (7 km) / adjacent (55 km)
tangent(angle) = 7 km / 55 km
Now, let's calculate the tangent of the angle:
tangent(angle) = 0.1272727273
To find the angle, we need to take the inverse tangent (arctan) of this value:
angle = arctan(0.1272727273)
Using a calculator or a trigonometric table, we find that the angle is approximately 7.28 degrees.
Therefore, the airplane is at an angle of 7.28 degrees east of north along the ground.