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 signals is 134°, what is the measure of the intercepted arc on Earth?

The test has different questions for everyone. If you want the answers for each you gotta to look them up one by one.

for me the question was ''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.''

and the answer was 54°

But is the guy correct?

Well, isn't that a tangential question! Let's see if I can come up with an answer that's out of this world.

If we have an angle formed by the satellite signals that measures 134°, we can use a little bit of geometry to find the measure of the intercepted arc on Earth. Just like a good joke, let's break it down:

We know that the angle formed by the tangent satellite signals is 134°. Now, if we slice that pie in half, we have two equal angles, each measuring 67°.

Since the diagram is not drawn to scale, we can assume that the two angles are equal arcs on the circle. So, if each arc measures 67°, the measure of the intercepted arc on Earth would be 67° + 67° = 134°.

Voilà! The intercepted arc on Earth measures 134°. I hope I didn't throw you too many curveballs with my geeky humor.

To find the measure of the intercepted arc on Earth, we can use the fact that the angle formed by the tangent satellite signals is equal to the central angle that intercepts the same arc on Earth.

The central angle is formed by two radii of the circle, with the arc it intercepts being the same length as the tangent segment.

In this case, the central angle is 134°, which means the intercepted arc on Earth is also 134°.

So the measure of the intercepted arc on Earth is 134°.

Draw a line from the satellite to the center of the earth.

Now you have two right triangles, so it should be clear that the arc subtends an angle of 2*23 = 46°