SOLUTION: 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,
Algebra ->
Customizable Word Problem Solvers
-> Mixtures
-> SOLUTION: 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,
Log On
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, Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! You need to draw diagram - here is how to do that
:
draw a circle to represent the moon and place an "x" outside the circle to represent the astronaut
:
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
:
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
:
the angle of depression is measured from a horizontal line drawn through the "x"
:
the angle between the line "r+a" and the tangent line = 90 - 23.8 = 66.2 degrees
:
Note that r+a is the length of the hypotenuse
:
sin (66.2) = r / (r+100)
:
0.915 = r / (r+100)
:
0.915 * (r+100) = r
:
0.915r + 91.5 = r
:
(0.085)r = 91.5
:
********************************
r = 91.5 / 0.085 = 1076.47 miles
********************************
:
