The moon is at a distance of 3.84 × 108 m from the Earth. If viewed

1.	The moon is at a distance of 3.84 × 108 m from the Earth. If viewed from two diametrically opposite points on the Earth, the angle subtended at the moon is 1° 54′. What is the diameter of the Earth?
Answer» Given, Distance (D) = 3.84 × 10⁸ m Subtended angle (α) = 1° 54′ = (60’+ 54′) = 114′ = 114 × 2.91 × 10^-4 rad = 3.317 × 10^-2 rad To find: Diameter of Earth (d) Formula: d = αD Calculation: From formula, d = 3.317 × 10^-2 × 3.84 × 10⁸ = 1.274 × 10⁷ m Diameter of Earth is 1.274 × 10⁷ m.

The moon is at a distance of 3.84 × 108 m from the Earth. If viewed from two diametrically opposite points on the Earth, the angle subtended at the moon is 1° 54′. What is the diameter of the Earth?

Answer»

Given,

Distance (D) = 3.84 × 10⁸ m

Subtended angle (α)

= 1° 54′ = (60’+ 54′) = 114′

= 114 × 2.91 × 10^-4 rad

= 3.317 × 10^-2 rad

To find: Diameter of Earth (d)

Formula: d = αD

Calculation: From formula,

d = 3.317 × 10^-2 × 3.84 × 10⁸

= 1.274 × 10⁷ m

Diameter of Earth is 1.274 × 10⁷ m.