Question

The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth’s surface. If the angle formed by the tangent satellite signals is 126°, what is the measure of the intercepted arc on Earth? The figure is not drawn to scale.

A. 252°
B. 108°
C. 63°
D. 54°

Answer 1

Option D. 54°

Explanation:

The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of the earth as shown in figure attached.

Angle formed by the tangent satellite signals is angle PSQ = 126°

As we know from outside angle theorem formed by tangents

m∠PSQ + m(minor arc PQ) = 180°

126° + m(PQ) = 180°

m(PQ) = 180 - 126 = 54°

Therefore answer is length of the intercepted arc will be 54°

Option D. 54° is the correct option

Answer 2

As given that
∠ASB = 126º, making the angular measure of the intercepted arc:
so

∠ACB = 180º - 126º = 54º = 3π/10
so correct option is D
hope it helps