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Boston, Mass. and Columbus,Ohio are about 800 miles apart. Find the angle (in radians and in degrees) made by two rays from the center of the earth through these two cities.

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Answer:

Angle, θ = 0.20207 Radian or 11.58°

Step-by-step explanation:

Distance between Boston, Mass and Columbus, Ohio= 800 miles

We known that the radius of the earth= 3959 miles

We known that,

⇒Arc length = theta × radius of earth

⇒(800) miles = θ × (3959) miles

⇒[tex]\dfrac{800}{3959}=\theta[/tex]

Therefore, θ = 0.20207 Radian

Now, converting this value in terms of degrees,

[tex]0.20207\times \dfrac{180}{\pi}\\\\=0.20207\times \dfrac{180}{3.14}\\\\=11.58^\circ[/tex]

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