Question

the moon is at a distance of 3.84 x 10 8m from the earth.if viewed from two diametrically opposite points on the earth,the angle subtended by the moon is 1degree 24minutes then what is the diameter of the earth?

Answer 1

first of all, converted angle subtended by the moon into radian.

we know, 180° = π rad

so, 1° = π/180 rad

and 60' = 1°

so, 24' = 1/60 × 24 = (2/5)°

and then, (2/5)° = π/180 × (2/5) rad

= π/180 × 2/5 = π/450 rad

so, 1° 24' = π/180 + π/450 = 7π/900 rad

now, using formula,

Φ = L/r

here, r = 3.84 × 10^8 m and L is the diameter of the earth.

so, 7π/900 = L/(3.84 × 10^8)

or, 7π × 3.84 × 10^8/900 = L

or, L = 9.38289 × 10^6 m

hence, if angle subtended by the moon is 1° 24' then, diameter of the earth is 9.38289 × 10^6 m

[ note : as we know, diameter of the earth is ~ 1.28 × 10^7 m. here we didn't get nearest value of it because of angle subtended by the moon is small. for getting perfect value angle should be 1°54" ]

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

☆☆Mark me brainliest☆☆