Question

an airplane is 5,000 feet above the ground, as shown in the picture below. its angle of descent for landing is 30 degrees. how far is the airplane from landing? 5,000 feet 5,500 feet 6,500 feet 10,000 feet 12,500 feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height (opposite side to the \(30^{\circ}\) angle) is \(h = 5000\) feet and we need to find the hypotenuse \(c\) (distance from the airplane to landing). Using the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin30^{\circ}=\frac{5000}{c}\).

Step2: Solve for \(c\)

Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{5000}{c}\). Cross - multiplying gives \(c = 5000\times2\).

Answer:

\(10000\) feet (the third option)