SOLUTION: radius of the earth A space lab circles the earth at an altitude of 380 miles. When an astronaut views the horizon of earth the angle theta is 65.8 degrees . use this information

Question 325067: radius of the earth
A space lab circles the earth at an altitude of 380 miles. When an astronaut views the horizon of earth the angle theta is 65.8 degrees . use this information to establish the radius of the earth.
The answer on the back of the book is 3944 miles.
I started by setting it up by perceiving that the line from the center of the earth to the space lab as being the radius minus 380 miles and if you were to draw another perpendicular line from the center of the earth at a 90 degree angle from the line that goes to the space lab. you'd be able to create a right triangle, and calculate it with the angle theta. but that still leaves me two variables. what am I not seeing that leads me to a real number type of answer?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you draw the picture, you should get

Looking at the drawing, we have a hypotenuse of miles and a leg of miles. Since this leg is the opposite leg with the given angle, this means that we can use the sine function. Recall that sin(theta) = opposite/hypotenuse

So

I'll let you continue. If you need more help, let me know.
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