Question

The moon subtends an angle 57 minutes at the base-line equal to the radius of the earth. What is the distance of the moon from the earth? [ Radius of the earth = 6.4×10]

Answer 1

Let the distance from the earth to the moon equals to D.

Convert the 57' min to Arc second

57 × 60 = 3420

Convert the arc second to radians :

1 s = 4.85 × 10⁻⁶ radians

3420 × 4.85 × `10⁻⁶ = 0.016587

Using the formulae :

D = R / Ф

Where R is the radius of the earth and Ф the arc able in radians.

Doing the substitution we have :

(6.4 × 10⁻⁶) / (0.016587) = 3.85 × 10⁻⁴

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Answer 2

Answer:

First convert minute into second

1'=60"

So, 57'= 3420" (57×60=3420)

1"=4.85×10^-6 rad.

So, 3420"= 3420×4.85×10^-6

=16587×10^-6 rad.

We know that theta=basis/D

So, D=basis/theta

Now put the values...

6.4×10^6 / 16587×10^-6

Now,( 6.4/16587) ×10^6+6

So, (0.000385844336) × 10^12

Now, we can write (0.000385844336) as (3.85/10^4)

(3.85) × 10^12-4

3.85×10^8...Ans!