Avoid Crashing into the Building: The Angle of Elevation Challenge!

What angle of elevation must the plane take off to avoid crashing into the building?

Given that an airplane takes off 200 yards in front of a 20 yards building, at what angle of elevation should the plane take off to clear the building successfully?

Angle of Elevation Calculation

To avoid crashing into the building, the airplane needs to take off at a specific angle of elevation. At this angle, the plane will safely clear the building without any collision.

To determine the angle of elevation that the plane must take off, we can utilize trigonometry. The tangent of the angle of elevation can be calculated using the formula tan(theta) = opposite/adjacent. In this scenario, the opposite side is the height of the building (20 yards) and the adjacent side is the distance between the plane and the building (200 yards).

By substituting the values, we get tan(theta) = 20/200 = 1/10. Taking the inverse tangent of 1/10 will give us the angle: theta = tan^(-1)(1/10).

Therefore, the plane must take off at an angle of approximately 5.71 degrees to avoid crashing into the building. At this angle, the airplane's flight path will ensure that it safely clears the building without any contact.

It is crucial for pilots to calculate and consider the angle of elevation during takeoff to prevent potential accidents or collisions with obstacles in the flight path. Safety measures and accurate calculations play a significant role in ensuring a successful and secure flight.