SOLUTION: A spacelab circles Earth at an altitude of 380 miles. When an astronaut views the horizon of Earth, the angle θ is 65.8 dgrees. Use this information to estimate the radius o
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Question 148221: A spacelab circles Earth at an altitude of 380 miles. When an astronaut views the horizon of Earth, the angle θ is 65.8 dgrees. Use this information to estimate the radius of the Earth.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A spacelab circles Earth at an altitude of 380 miles. When an astronaut views the horizon of Earth, the angle θ is 65.8 dgrees. Use this information to estimate the radius of the Earth.
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Draw an arc of the earth; Draw a radius from the center then thru the arc
to a point 380 miles above the arc.
Draw a tangent from the top of the previous segment to a point that
is tangent to the arc.
Draw a radius from the center to the point of tangency (that should form
a right angle at the point of tangency).
Label the angle of depression from the spacelab 65.8 degrees.
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EQUATION:
sin(65.8) = r / (r+380)
0.91212(r+380) = r
0.91212r + 346.6056 = r
346.6056 = 0.08788r
r = 3944.078.. miles
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Cheers,
Stan H.
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