The farthest distance a satellite signal can directly reach is the length of the line segment tangent to the curve of the Earth's surface.
A sphere is shown with two points unlabeled. One line lies on the sphere connected through the unlabeled point. A second line lies on the sphere connected through the second unlabeled point. The lines connect at a point labeled satellite.
If the angle formed by the tagent satellite signals is 126 ° , what is the measure of the intercepted arc on Earth?
(1 point)
Responses
180°180degree
64°64degree
54°54degree
22°
To find the measure of the intercepted arc on Earth, we need to find the angle at the center of the circle that corresponds to the tangent angle of 126°.
The angle at the center of the circle is twice the angle formed by the tangent satellite signals. Therefore, the angle at the center of the circle is 2 * 126° = 252°.
Since the intercepted arc on Earth is the same measure as the central angle, the measure of the intercepted arc on Earth is 252°.
Therefore, the correct answer is 180°.