Question

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.

Answer 1

Angle, θ = 0.20207 Radian or 11.58°

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

⇒
`(800)/(3959)=\theta`

Therefore, θ = 0.20207 Radian

Now, converting this value in terms of degrees,

`0.20207* (180)/(\pi)\\\\=0.20207* (180)/(3.14)\\\\=11.58^\circ`