Rouieres Tests MATH 112800 Plane Tngonometry Fall 2016 a Tak

Rouieres Tests MATH 112-800 Plane Tngonometry Fall 2016 a Take Test-Edward White-Internet Explorer https www.mathul.com/student Player MATH 112-0 Plane Tngonomety Fa 2016 Fest: Final Exam 39 of 45 complete The figure shows a satellite dinding 115 miles above a planet When the satellite is drecty above pont B, angle A measures 76.2 Find the planer\'s radius The radius of the planetis approximately maes Round to nearest mile as needed) Enter your answer inthe answer box 127 16 831 PM Time Remaining: 002721 Submr Tes This Test: 45 pts possb

Solution

Two things to notice from the diagram.
a) There\'s a 90 degree angle, so basic trig functions can be used.
b) The radius from B to the center of the circle is the same as thr radius
from the center of the circle to the right angle.

Let\'s call the radius \"r\"
Since we have a right triangle involved here,
Sin \"alpha\" = opposite / hypotenuse
Sin 76.2° = r /( r+115 )
0.97113=r / (r+115)
0.97113(r+115)=r
0.97113r+111.67995=r
0.974r-r= -111.67995
-0.02887r= -111.67995
r=-111.67995 / -0.02887
r = 3868.37 miles
r = 3868 miles, (rounded )