Question

The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth's surface. The diagram is not drawn to scale.
If the angle formed by the tangent satellite signal is 154°, what is the measure of the intercepted arc on Earth?
26°
52°
77°
308°

Answer 1

To solve the question, we draw a circle representing a great-circle section of the earth, with satellite at a point S above earth. Draw tangents from S to he circle, and from points A and B, to the center C.
Hence:
AC and BC are radii, and
SA⊥AC and SB⊥BC
∠ASB=154°
making the angular measure of the intercepted arc:
∠ACB=180-154=26°

Answer: 26°