Questions: To approach the runway, a pilot of a small plane must begin a 5° descent starting from a height of 163 mile, how many miles from the runway is the airplane at the start of this approach?

To approach the runway, a pilot of a small plane must begin a 5° descent starting from a height of 163 mile, how many miles from the runway is the airplane at the start of this approach?

Transcript text: To approach the runway, a pilot of a small plane must begin a $5^{\circ}$ descent starting from a height of 163 mile, how many miles from the runway is the airplane at the start of this approach?

Solution

Solution Steps

Step 1: Draw the diagram

We are given a right triangle where the height is 1639 ft and the angle of descent is 5°. We want to find the horizontal distance, which we label as _x_.

Step 2: Convert feet to miles

Since the answer choices are in miles, we convert the height to miles using the conversion factor 1 mile = 5280 ft:

1639 ft * (1 mile/5280 ft) = 0.31041666... miles ≈ 0.310 miles

Step 3: Use trigonometric ratios

We can use the tangent function to relate the angle, the opposite side (height), and the adjacent side (horizontal distance _x_).

tan(5°) = opposite/adjacent = height/x

tan(5°) = 0.310 miles/x

Step 4: Solve for x

x = 0.310 miles / tan(5°)

x ≈ 0.310 miles / 0.0874886...

x ≈ 3.545 miles

Step 5: Round to nearest tenth