Question

The moon is observed from two diametrically opposite points A and B on earth. The angle subtended at the moon by two direction is 1⁰54'. Given diameter of earth is 1.276× 10 to power 7m compute the distance of moon from earth ​

Answer 1

Answer

• Distance of Moon from the Earth is appoximately equal to 3.753 × 10⁸ metres.

Explanation

GIVEN :

Moon is observed from two diametrically opposite points A and B on Earth. The angle subtended on the moon by two directions is 1°54'. Given the diameter of Earth is 1.276 × 10⁷ m

• Diameter of Earth; d = 1.276 × 10⁷ m
• Angle subtended on moon from A and B two diametrically opposite points on Earth; θ = 1°54'

TO FIND :

• Distance of moon from the Earth; s = ?

SOLUTION :

• Calculating Angle θ into Radians

$\implies$ θ = 1° 54'

Since, 1° = 60'

therefore,

$\implies$ θ = 1° + (54 / 60)°

$\implies$ θ = (115/60)°

$\implies$ θ = (23 / 12)°

Now, since 1° = π / 180  Rad

therefore,

$\implies$ θ = (23/12) × (π/180)

$\implies$ $\underline{\underline{\sf{\theta=0.034\;\;Rad}}}$

• Calculating distance of moon from Earth

Using relation

$\implies$ θ = d / s

$\implies$ 0.034 = (1.276 × 10⁷) / s

$\implies$ s = (1.276 × 10⁷) / 0.034

$\implies$ s = 3.753 × 10⁸  m [ Approx. ]

therefore,

• Distance of Moon from the Earth is appoximately equal to 3.753 × 10⁸ metres.

Answer 2

$\huge\star\underline\mathfrak\red{Answer:-}$

Solution:

Angle subtended

theta = 1° 54' = 114' = 114 × 2.19 × 10^-4 rad

= 3.317 × 10^-2 rad

Diameter of earth= theta × distance to the moon from the earth

= 3.317 ×10^-2 × 3.84×10^8 m

= 1.274× 10^7 m