We are given that the angle of descent is 2 degrees, and the airplane traveled 6 more miles after crossing the bridge. Let's call the height of the airplane at the point it crosses the bridge "h", and the horizontal distance from the airplane to the bridge "d".
We can use the tangent function to relate the angle of descent to the height and distance:
tan(2°) = h / (d + 6)
Rearranging this equation, we get:
h = (d + 6) tan(2°)
We are also given that the height of the bridge above the water is 212 feet. So the height of the airplane above the water at the point it crosses the bridge is:
h + 212
To find the height above the bridge, we need to subtract the height of the bridge:
h + 212 - 212 = h
Substituting the expression for h, we get:
h = (d + 6) tan(2°)
To find d, we need more information. However, we can use the fact that the airplane passed less than 900 feet above the bridge to estimate a maximum value of d:
tan(2°) = h / (d + 6)
h = 900 feet
Substituting these values, we get:
tan(2°) = 900 / (d + 6)
d + 6 = 900 / tan(2°)
d = 900 / tan(2°) - 6
Using a calculator, we get:
d ≈ 19294.4 feet
Substituting this value for d in the expression for h, we get:
h ≈ 670.1 feet
So the airplane crossed the George Washington Bridge at a height of approximately 670.1 feet above the water.
To find the clearance over the bridge, we subtract the height of the bridge from the height of the airplane:
670.1 - 212 = 458.1 feet
So the airplane cleared the bridge by approximately 458.1 feet.
The calculation does not support the statement that the airplane passed less than 900 feet above the bridge, since the clearance was more than 900 feet.