A plane is descending at a
19°
angle of depression. If the current altitude of the plane is 1,250 feet, find the distance the plane still needs to fly to reach the ground (flight path distance, not ground distance).
Let x be the distance the plane still needs to fly to reach the ground.
In a right triangle formed by the plane, the ground, and the line of sight, the angle of depression is 19°.
The opposite side of the angle of depression is the altitude of the plane, which is 1,250 feet.
Using the tangent function, tan(19°) = 1,250 / x.
Simplifying the equation, tan(19°) = 1,250 / x.
Multiply both sides of the equation by x to isolate the variable, x.
x * tan(19°) = 1,250.
Divide both sides of the equation by tan(19°) to solve for x.
x = 1,250 / tan(19°).
Using a calculator, the value of x is approximately 3,777.5 feet.
Therefore, the plane still needs to fly approximately 3,777.5 feet to reach the ground.