Question

Help on math? :)

Answer 1

1. Let O be the center of the sphere, A the tangency point and B the location of the satellite. (as in the figure below)

2. Join B to O. M(ABO)=$\frac{1}{2}$m(B)=(1/2)*138°=69°.


3. m(OAB)=90° as a radius to a tangency point is perpendicular to the tangent at that point. 

4. m(AOB)=180°-90°-69°=21°.

5. check picture 2. Arc AM is equal to the measure of the central angle AOM = 21°.

6. The measure of the intercepted arc is 21°*2=42°