The moon's distance from the earth is 360000 km and its diameter subtends an angle of 31' at the eye of the observer on the earth. Find the radius of the moon.
2007-05-31 19:15:21 · 5 answers · asked by g 2 in Science & Mathematics ➔ Mathematics
Since the moon is very far away, its diameter can be considered to be an arc with the distance between the moon and earth as radius.
now,31'=31/60 degree=(31/60)*(pi/180) radians
so,diameter of the moon / distance from earth
= d/360000=(31/60)*(pi/180)
or, d=(360000*31*22) / (60*180*7) [taking pi as 22/7]
or, d=245520000/75600
or, d=3247.619047 619047 619047 619...
or, d=3247.62 km {approximately}
so, the diameter of the moon is 3247.62 km.
so, radius of the moon= 1623.81 km.
2007-06-01 14:18:52 · answer #1 · answered by Happy 3 · 0⤊ 0⤋
picture a right triangle, eye to moon center to moon edge,
r/360000 = tan 31/60°
r = 360000(0.0090177789)
r = 3246.4 km
2007-05-31 19:23:14 · answer #2 · answered by Philo 7 · 0⤊ 0⤋
using the arc longitude equation:
arc=radius*angle
in this case radius=distance from the earth.
assuming the arc like a line:
arc=moon's diameter
angle=31' (need to be in radians)
transforming 31' to sexagesimal degrees:
(1deg*31')/60 = 0.51deg
now use it in the equation:
moon's radius=(moon's diameter)/2
including the transformation of 0.51 deg to radians we got:
moon's radius=(arc)/2=360000 km*0.51*pi/(180*2)
finally:
moon's radius=576504/360=1601.4km approximately
La Luna tiene un radio de 1736,6 km
2007-05-31 19:43:29 · answer #3 · answered by LENNONLNX0618 2 · 0⤊ 0⤋
r / 360000 = tan((31 / 2) / 60)
r = 360000 tan(31 / 120) = 1623.1672...
r is approximately 1623 km.
2007-05-31 19:41:40 · answer #4 · answered by Loong 2 · 0⤊ 0⤋
why don't you just make a search for the moon on wikedpidia, and you'll know all about it. Then use that number to see how your numbers fit in.
2007-05-31 19:19:35 · answer #5 · answered by Renegade 3 · 0⤊ 0⤋