Question

Find the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)

Answer 1

Answer:

6.914miles (to 3 decimal places)

Step-by-step explanation:

Length of an arc = θ/360 *2πr

angle subtended by arc at the center of the earth = 6 minutes

1 minute =1/60 degree

6 minute= 6/60 degree =0.1°

θ=0.1°

radius of earth = 3960 miles

distance along the arc = $\frac{0.1}{360}*2\pi *3960$

    =6.9142857143miles

Answer 2

The distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles

The length of an arc that subtends with a central angle of Θ in degree is given by:

arc length = (Θ/360) * 2πr

where r is the radius of the circle

Given that r = 3960 miles, θ = 6 minutes = (1/60 degree) * 6 = 1/10 degree

Therefore:

arc length = (1/10 ÷ 360) * 2π(3960) = 6.912 miles

Hence the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles

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