College

If \(\theta = 33^\circ\), find the distance between two cities, A and B, to the nearest mile. The radius of the Earth is approximately 4000 miles.

Answer :

Answer:

The distance between the two cities is 2304 miles.

Step-by-step explanation:

Step 1: Convert Degrees to Radians

The formula for converting degrees to radians is:

(radians)=(degrees)*(π/180)

Given = 33∘, the conversion is:

θ(radians) =33× (π/180) = 0.57596radians

Step 2: Use the Arc Length Formula

The radius of the Earth is = 4000 miles. Plugging the values into the formula:

Distance=4000×0.57596=2303.84miles

Step 3: Round to the Nearest Mile

Distance≈2304miles

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