document.write( "Question 1068100: An astronaut circling the moon at an altitude of 100mi notes that the angle of depression of the horizon is 23.8°. what is the radius of the moon? please help, \n" ); document.write( "

Algebra.Com's Answer #683285 by rothauserc(4718) $\"\"$ $\"About$

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You need to draw diagram - here is how to do that
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\n" ); document.write( "draw a circle to represent the moon and place an \"x\" outside the circle to represent the astronaut
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\n" ); document.write( "draw a line from the center of the circle to the \"x\", the length of this line is radius of the moon(r) + the altitude(a) of the astronaut above the moon
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\n" ); document.write( "draw a line from the \"x\" to a point tangent to the circle and draw another line from the center of the circle to the point of tangency, label this line r
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\n" ); document.write( "the angle of depression is measured from a horizontal line drawn through the \"x\"
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\n" ); document.write( "the angle between the line \"r+a\" and the tangent line = 90 - 23.8 = 66.2 degrees
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\n" ); document.write( "Note that r+a is the length of the hypotenuse
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\n" ); document.write( "sin (66.2) = r / (r+100)
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\n" ); document.write( "0.915 = r / (r+100)
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\n" ); document.write( "0.915 * (r+100) = r
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\n" ); document.write( "0.915r + 91.5 = r
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\n" ); document.write( "(0.085)r = 91.5
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\n" ); document.write( "r = 91.5 / 0.085 = 1076.47 miles
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