Question

the moon distance from the Earth is 3 ,60,000 km and its diameter subtends an angle of 31 minute at the eye of the observer . find the diameter of the moon. guys pls give answer ​

Answer 1

Let AB be the diameter of moon.

we can consider the diameter of moon as arc because the distance between the earth and moon is large.

Let E be the observer.

Let d be the diameter of moon .

Then d=arcAB.

θ=42°

=(42/60)°

=[(42/60)xπ/180]

r=360000kms

θ=arc/radius

[(42/60)xπ/180]=d/360000

d=[42/60)xπ/180]x360000

d=0.7x0.017x360000=4398 km.

but the the actual diameter of moon is 3474km.

so in the given question the data is given wrong