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You can use trig here
@jayzdd Do I use sine law or cosine law for this question?
radius of earth is about 6,371 km
here is a better picture http://prntscr.com/9erkac
lets use law of sines
sin(24) / 6371 = sin(x) / ( 980 + 6371)
okay so... 980 +6371 =7351 7351(sin24) / 6371
@jayzdd am i right so far?
yes, now take inverse sine
now what do i do?
distance= rate* time
which number is the rate and which is the time?
rate is the speed at which light travels
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.
i mean we did the law of sines correctly, but there are two solutions to this triangle
the angle made by the satellite and the center of the earth is an obtuse angle
How do I find it?
we can subtract 180 from the angle we got before
180-27.9 = 152.1
correct, and then we can use law of sines again to find the length from the satellite to the dish
find the third angle, 180 - 152.01 - 24 = 3.9889 then use law of sines alternatively you can use law of cosines
6371 / sin(24) = x / sin 3.99 x = sin(3.99)* 6371 / sin(24)
x = 1089.63
@jayzdd Is 1089.63 our final answer?
nope, thats just the distance from the satellite to the dish in km
Ah okay, so what's the next step?
we want to find the time it takes to travel that distance d = r* t 1089.63 * 1000 meters = (3x 10^8 meters) * t
1089.63*1000 / ( 3*10^8) = time in seconds
0.004 seconds, to the nearest thousandth
some books use 6400 km for the radius of the earth, we need that number does your book give a radius for earth?
@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
yes thats correct 3.6321x10^-03 =3.6321x10^-3 = 0.0036321 ~ 0.004
i redid the problem using the radius of 6400 km it comes out to the same answer of 0.004 seconds
Interestingly, suppose you did the problem using law of cosines from the beginning. Do you see that you would have two solutions?
Haha yes I do see that