Question

To approach the runway, a pilot of a small plane must begin a 10 degrees descent starting from a height of 1983 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

Answer 1

2.2 miles

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

We are given an angle (10°) and its opposite side length (1983 ft), and we are asked to find the hypotenuse (the straight-line distance from the plane to the runway).

... sin(10°) = (1983 ft)/distance

Multiplying by distance and dividing by sin(10°), we have ...

... distance = (1983 ft)/sin(10°) ≈ 11419.6 ft

We want to express this in miles, so we have ...

... 11419.6 ft = (m mi)×(5280 ft/mi)

... (11419.6 ft)/(5280 ft/mi) = m mi ≈ 2.163 mi

Rounding to tenths, the distance is ...

2.2 miles

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Comment on the question

The distance from the plane to the airport is different than the horizontal distance from the airport at which the descent must start. The latter distance is the "adjacent" leg of the triangle, so must be found using the tangent function. Rounded to tenths, it is 2.1 miles.