The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth's surface

Question

2 years ago

10

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°

Mathematics

1 answer:

konstantin123 [22] · Answer 1 · 2023-10-08T21:04:42+03:00

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°