To approach the runway, a pilot of a small plane must begin a 20° descent starting from a height of 3,760 feet above the ground
It
It
20°
3,760 fi
It
It
To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? The figure is not drawn to scale.
(1 point)
10.993.5 ml
• 2.1 mi
• 1.8 mi
• 0.8 mi
To solve this problem, we can use trigonometry. We know that the plane is descending at a 20° angle and the height of the plane is 3,760 feet.
We can use the tangent function to calculate the distance from the runway:
tangent(20°) = opposite/adjacent
Let x be the distance from the runway.
tangent(20°) = 3760/x
To find x, we can isolate it:
x*tangent(20°) = 3760
x = 3760/tangent(20°)
Using a calculator, tangent(20°) is approximately 0.36397.
x = 3760/0.36397
x ≈ 10.352
Thus, the airplane is approximately 10.4 miles from the runway at the start of this approach.