Satellite geometry physics problem

AI Thread Summary
To determine the angle above the horizon for communication with a geosynchronous satellite over the equator at the same longitude as Seattle, the problem involves applying the law of sines and cosines. The radius of the Earth is given as 6.38×10^6 m, while the radius of the satellite's orbit is 3.58×10^7 m. A triangle was drawn to visualize the problem, and there is uncertainty about whether the angle formed by the tangent line and the Earth's radius is a right angle. The user attempted to set up the equation using sine functions but expressed confusion about solving for the angle x. A scientific calculator is necessary to find the cosine inverse for the calculations.
linnus
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Homework Statement



A geosynchronous satellite is stationary over a point on the equator (zero degrees latitude) at the same longitude as Seattle, Washington. Seattle's latitude is 47.6°. If you want to communicate with the satellite, at what angle above the horizon must you point your communication device? The Earth's radius is 6.38×10^6 m. Hint: You will also need the law of sines and the law of cosines.

Homework Equations



Sin angleA/A=sin angleB/B
radius of a geosynchronous satellite= 3.58e7 meters

The Attempt at a Solution


I drew a triangle- a quick question would the angle at which the line tangent to the surface and the radius of the Earth be a right angle?

I got
sin(90+x)/3.58e7=sin(42.4)/6.38e6
I'm not sure how to solve for x here...and I don't think this equation is right...
 
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well I don't know if the equation is correct or not, but for finding x,

sin(90+x)=cos x ...This is an identity. You will need a scientific calculator to find cos inverse.
 

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