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• Mar 1st 2010, 03:42 PM
Hi purplec16,

The horizon makes a 90 degree angle with the Earth's centre.
This is because the astronaut's line of sight makes a tangent with the planet
(if you balance a perfectly round ball on a table, it's centre is directly above the point of contact or tangency).

The triangle has the same sides and angles,
so the trigonometry works exactly as skeeter originally outlined.

$\displaystyle Sin(65.8^o)=\frac{opposite}{hypotenuse}=\frac{R}{R +380}$

$\displaystyle (R+380)Sin(65.8^o)=R$

$\displaystyle RSin(65.8^o)+380Sin(65.8^o)=R$

$\displaystyle 380Sin(65.8^o)=R-RSin(65.8^o)=R[1-Sin(65.8^o)]$

$\displaystyle R=\frac{380Sin(65.8^o)}{1-Sin(65.8^o)}$
• Mar 1st 2010, 04:04 PM
purplec16
Sorry Skeeter, my mistake 380 miles is correct
• Mar 1st 2010, 04:16 PM
purplec16
Thank you so much, I get it now and I completely understand, Thank you Skeeter and Archie
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