Question

Find the distance along an arc on the surface of the earth that subtends a central angle of 2 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles

Answer 1

Answer:

2.3 miles

Step-by-step explanation:

step 1

Find the circumference of the earth

The circumference is equal to

$C=2\pi r$

we have

$r=3,960\ miles$

assume

$\pi =3.14$

substitute

$C=2(3.14)(3,964)=24,893.92\ mi$

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find out the arc length on the surface of the earth that subtends a central angle of 2 minutes

Remember that

$1^o=60'$

so

$360^o=360(60)=21,600'$

Applying proportion

$\frac{24,893.92}{21,600}\ \frac{miles}{minutes}=\frac{x}{2}\ \frac{miles}{minutes}\\\\x=24,893.92(2)/21,600\\\\x=2.3\ miles$