To approach a runway, a plane must began a 7 degree descent starting from the height of 2 miles above the ground. To the nearest mile, how many miles from the runway is the airplane at the start of this approach?
draw a diagram. If the required distance is d,
2/d = tan7°
d = 16.3 miles
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To find the distance from the runway at the start of the approach, we can use trigonometry. In this case, we have the height of the plane and the angle of descent.
First, we need to convert the descent angle from degrees to radians. To do this, we multiply the angle (7 degrees) by π/180 to get the angle in radians.
Angle in Radians = 7 * (π/180) = 7π/180 radians.
Next, we can use the tangent function to find the distance from the runway. The tangent of an angle is defined as the ratio of the opposite side (height of the plane) to the adjacent side (distance from the runway).
Tangent(Descent Angle) = Opposite side (Height of the plane) / Adjacent side (Distance from the runway).
Rearranging the equation, we get:
Distance from the runway = Height of the plane / Tangent(Descent Angle).
Now let's calculate the distance from the runway:
Given:
Height of the plane = 2 miles
Descent angle (in radians) = 7π/180 radians
Distance from the runway = 2 miles / tan(7π/180)
Using a calculator, we find that tan(7π/180) ≈ 0.1227849.
Substituting the value of the tangent, we have:
Distance from the runway ≈ 2 miles / 0.1227849
Calculating this division, we get:
Distance from the runway ≈ 16.28 miles.
Therefore, to the nearest mile, the airplane is approximately 16 miles from the runway at the start of the approach.