Question

two cities, a and b, are 5500 miles apart. the radius of the earth is approximately 4000 miles. express angle θ in radians and in degrees. express angle θ in radians. θ = radians (type an integer or a decimal.)

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc \( s \) is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians. We need to solve for \( \theta \), so we can rearrange the formula to \( \theta=\frac{s}{r} \).

Step2: Identify the values of \( s \) and \( r \)

Here, the arc length \( s \) (the distance between the two cities) is 5500 miles, and the radius \( r \) of the Earth is 4000 miles.

Step3: Calculate \( \theta \) in radians

Substitute \( s = 5500 \) and \( r = 4000 \) into the formula \( \theta=\frac{s}{r} \). So, \( \theta=\frac{5500}{4000} \). Simplifying this fraction, we get \( \theta = 1.375 \) radians.

Answer:

\( \theta = 1.375 \) radians