The mean diameter of Earth is 7926 miles. Use the conversion factor 1.6093 to convert miles to kilometers, and divide by 2 to get the mean radius of Earth. The mean radius to the nearest kilometer is _____ kilometers.
Hint: Label the diagram with the radius in the two appropriate places to help you answer the next questions.
A)3,963
B)12,756
C)4,925
D)6,378
The central angle defines the arc of the satellite's movement from the 30º point to a point overhead. If you find the central angle, you can compute the time it takes the satellite to travel the arc of the orbit. The measure of the central angle is ____ .
Hint: Use the Law of Sines (A/sin A = B/sin B = C/sin C) to find the measure of angle A, then use the Law of Sines again to find the measure of angle B.
B)30º
C)120º
D)88º
What time will the satellite pass through the beam of the antenna?
A)11:53 am
B)11:45 am
C)Noon
D)11:36 am
+33652 mean radius R = 7926*1.6093/2 = 6378 km to nearest km.
Angle C = 90°+30° = 120°
legnth AB = 6378 + 2000 = 8378 km
sin(A)/6378 = sin(C)/8378 so sin(A) = sin(C)*6378/8378 = sin(120°)*6378/8378 = 0.69529
Angle A = sin-1(0.69529) ≈ 41°
Angle B = 180° - C - A = 180° - 120° - 41° = 19°
B/360° = t/2 where t is time in hours
t = 2*19/360 hrs = 0.19hrs
t = 6.333... mins = 6 mins 20 secs
12 noon - 6.33 mins = 11.53am + 40 secs.
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+33652 mean radius R = 7926*1.6093/2 = 6378 km to nearest km.
Angle C = 90°+30° = 120°
legnth AB = 6378 + 2000 = 8378 km
sin(A)/6378 = sin(C)/8378 so sin(A) = sin(C)*6378/8378 = sin(120°)*6378/8378 = 0.69529
Angle A = sin-1(0.69529) ≈ 41°
Angle B = 180° - C - A = 180° - 120° - 41° = 19°
B/360° = t/2 where t is time in hours
t = 2*19/360 hrs = 0.19hrs
t = 6.333... mins = 6 mins 20 secs
12 noon - 6.33 mins = 11.53am + 40 secs.
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