Question

The moons distance from Earth is 350000 km and it's diameter subtends an angle of 31' at the eye of the observer. The diameter of the moon is.

Answer 1

diameter= 2*radius

diameter = 2*350000

diameter = 700000

Answer 2

AnswEr:

• Let AB be the diameter of the moon .

• Let E be the eye of the observer.

Since the distance between the Earth and the moon is quite large, so we take diameter AB as arc AB .

• Let d be the diameter of the moon.

Then, d = arc AB .

We have,

$\\ \tt \: \: \: \: \theta \: = 31' = ( \frac{31}{60} ) \degree = ( \frac{31}{60} \times \frac{\pi}{180} ) {}^{c} \\ \\ \tt \: \: \: \: and \: \: r = 360000 \: kms \\ \\ \\ \therefore \tt \: \theta = \sf\frac{arc}{radius} \\ \\ \\ \implies \tt \: \: \frac{31}{60} \times \frac{\pi}{180} = \frac{d}{360000} \\ \\ \\ \implies \tt \: d = ( \frac{31}{60} \times \frac{\pi}{180} \times 360000) \: km \: \\ \\ \\ \implies \tt \blue{ 3247.62 \: kms}$

Hence, the diameter of the moon is 3247.62 kms.