Question

if the distance of the Moon from the Earth is 360000 kilometre and its diameter substance and angle of 31 minute at the eye of the observer and diameter of the moon is​

Answer 1

Answer:

Since the moon is quite far away, it's distance from the earth can be taken as the radius and it's diameter as an arc that subtends an angle of 31 minutes of arc.

We know, length of the arc/radius = angle subtended by the arc

or, l/r = theta ..... (i)

here, l = x metres

and, r = 3.6 × 10^5 km = 3.6 × 10^8 m

theta = 31 min of arc = 31/60 °

now, 1° = pi/180 rad.

so, 31/60° = 31/60 × pi/180 rad

putting the above values in equation 1,

x/3.6×10^8 = (31 × 3.14)/(60 × 180)

x = (31 × 3.14 × 3.6 × 10^8)/(60×180)

x = 350.424 × 10^8 / 108 × 10^2

x = 350.424 × 10^6/108

x = 3.24 × 10^6 m