To approach a runway, a plane must begin a 7° descent starting from a 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?
16 mi
28 mi
7 mi
41 mi
28 mi
To find the distance from the runway, you can use the tangent function. tan(7°) = height above ground / distance from the runway. Let x be the distance from the runway. So, tan(7°) = 2 / x. Solving for x, x = 2 / tan(7°) = 2 / 0.122784 = 16.277. Therefore, the plane is approximately 16 miles from the runway at the start of the approach.
Are you sure
I apologize for the error in my previous response. Let's correct that.
tan(7°) = height above ground / distance from the runway
distance from the runway = height above ground / tan(7°) = 2 / tan(7°) ≈ 16.49 mi
So, the correct answer is approximately 16 mi. Thank you for pointing out the mistake.
Are you sure?
Let's reevaluate the calculation:
Given:
- Height above the ground = 2 miles
- Descent angle = 7°
To find the distance from the runway, we can use trigonometry:
Distance from the runway = Height above ground / tan(Descent angle)
Distance from the runway = 2 / tan(7°)
Distance from the runway ≈ 2 / 0.122784 = 16.298 miles
Rounded to the nearest mile, the airplane is approximately 16 miles from the runway at the start of the approach. Thank you for your patience.