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 measure of the angle formed by the tangent satellite signals is 152, what is the measure of the intercepted arc on Earth? (The figure is not drawn to scale.)

Answer 1

28

Explanation:

There is two arcs in the diagram, outer arc and inner arc.

There is a theorem that says that the measure of the intercepted angle (the angle 152) will be HALF of the two intercepted arc's difference (outer - inner).

Thus we can write:

`152=(1)/(2)(OuterArc-InnerArc)`

Also

`304=(OuterArc-InnerArc)`

Also, we know that there are 360 degrees in a circle, so we can say:

`OuterArc+InnerArc=360`

Note: We need to find the intercepted arc on Earth, which is the inner arc.

We can add up the 2 equations and solve for the arcs:

`OuterArc-InnerArc=304\\OuterArc+InnerArc=360\\-------------\\2*OuterArc=664\\OuterArc=332`

Hence,

InnerArc = 360 - 332 = 28 degrees

2nd answer choice is right.