Satellite geometry physics problem

[linnus]

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...

 

[Google_Spider]

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.