On math? : )

if the angle formed by the tangent satellite signals is 138 degrees, what is the measure of the intercepted arc on earth?

the farthest distance a satellite signal can directly reach is the length of the segment tangent (l to the curve of earth's surface. the diagram is not drawn to scale.

a. 84 degrees

b. 276 degrees

c. 42 degrees

d. 69 degrees

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)=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°