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 = 1.375 radians (type an integer or a decimal.) express angle θ in degrees. θ = □° (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall the conversion formula from radians to degrees

The formula to convert radians to degrees is $\theta_{degrees} = \theta_{radians} \times \frac{180^\circ}{\pi}$.

Step2: Substitute the given radian value

We know that $\theta_{radians} = 1.375$. So we substitute this into the formula: $\theta_{degrees} = 1.375\times\frac{180^\circ}{\pi}$.

Step3: Calculate the value

First, calculate $1.375\times180 = 247.5$. Then divide by $\pi$: $\frac{247.5}{\pi}\approx\frac{247.5}{3.1416}\approx78.78$.

Answer:

$\theta \approx 78.78^\circ$