shelby1290
  • shelby1290
A satellite dish is orbiting the earth 980km above earth's surface. A receiving dish is located on earth such that the line from the Satellite to the dish and the line from the satellite to earth's centre form an angle of 24 degrees. If a signal from the Satellite travels at 3x10^8 m/s, how long does it take to reach the dish? Round your answer to the nearest thousandth of a second.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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shelby1290
  • shelby1290
anonymous
  • anonymous
You can use trig here
shelby1290
  • shelby1290
@jayzdd Do I use sine law or cosine law for this question?

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anonymous
  • anonymous
radius of earth is about 6,371 km
anonymous
  • anonymous
here is a better picture http://prntscr.com/9erkac
anonymous
  • anonymous
lets use law of sines
shelby1290
  • shelby1290
Okay
anonymous
  • anonymous
sin(24) / 6371 = sin(x) / ( 980 + 6371)
shelby1290
  • shelby1290
okay so... 980 +6371 =7351 7351(sin24) / 6371
shelby1290
  • shelby1290
x=0.469
shelby1290
  • shelby1290
@jayzdd am i right so far?
anonymous
  • anonymous
yes, now take inverse sine
shelby1290
  • shelby1290
x=sin-1(0.469) x=27.9
shelby1290
  • shelby1290
now what do i do?
anonymous
  • anonymous
distance= rate* time
shelby1290
  • shelby1290
which number is the rate and which is the time?
anonymous
  • anonymous
rate is the speed at which light travels
anonymous
  • anonymous
but i dont think we did the law of sines correctly. note that this is a 'angle side side' case, and its an ambiguous case, there are two solutions.
anonymous
  • anonymous
i mean we did the law of sines correctly, but there are two solutions to this triangle
anonymous
  • anonymous
the angle made by the satellite and the center of the earth is an obtuse angle
anonymous
  • anonymous
http://prntscr.com/9ersnt
shelby1290
  • shelby1290
How do I find it?
anonymous
  • anonymous
we can subtract 180 from the angle we got before
shelby1290
  • shelby1290
180-27.9 = 152.1
anonymous
  • anonymous
correct, and then we can use law of sines again to find the length from the satellite to the dish
anonymous
  • anonymous
|dw:1450255733811:dw|
anonymous
  • anonymous
find the third angle, 180 - 152.01 - 24 = 3.9889 then use law of sines alternatively you can use law of cosines
anonymous
  • anonymous
|dw:1450255928818:dw|
anonymous
  • anonymous
6371 / sin(24) = x / sin 3.99 x = sin(3.99)* 6371 / sin(24)
anonymous
  • anonymous
x = 1089.63
shelby1290
  • shelby1290
|dw:1450256163500:dw|
shelby1290
  • shelby1290
@jayzdd Is 1089.63 our final answer?
anonymous
  • anonymous
nope, thats just the distance from the satellite to the dish in km
shelby1290
  • shelby1290
Ah okay, so what's the next step?
anonymous
  • anonymous
we want to find the time it takes to travel that distance d = r* t 1089.63 * 1000 meters = (3x 10^8 meters) * t
anonymous
  • anonymous
1089.63*1000 / ( 3*10^8) = time in seconds
anonymous
  • anonymous
0.0036 seconds
anonymous
  • anonymous
0.004 seconds, to the nearest thousandth
anonymous
  • anonymous
some books use 6400 km for the radius of the earth, we need that number does your book give a radius for earth?
shelby1290
  • shelby1290
@jayzdd Thank you! That's the right answer! My textbook doesn't give me the radius of the earth for this question. What you see in the picture is exactly what's in my textbook. Oh and for this part... 1089.63*1000 / ( 3*10^8) = time in seconds I'm not sure if i'm doing it correctly but my calculator got 3.6321x10^-03
anonymous
  • anonymous
yes thats correct 3.6321x10^-03 =3.6321x10^-3 = 0.0036321 ~ 0.004
anonymous
  • anonymous
i redid the problem using the radius of 6400 km it comes out to the same answer of 0.004 seconds
anonymous
  • anonymous
Interestingly, suppose you did the problem using law of cosines from the beginning. Do you see that you would have two solutions?
shelby1290
  • shelby1290
Haha yes I do see that
anonymous
  • anonymous
|dw:1450258188924:dw|

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