Question

if the angle formed by the tangent satellite signals is 142 degrees what is the measure of the intercepted arc on earth

Answer 1

To find the measure of the intercepted arc on Earth, we first need to determine the central angle formed by the tangent satellite signals. The central angle is always twice the angle formed by the tangent lines.

Central angle = 142 x 2 = 284 degrees

Now, we can use the formula for the measure of an intercepted arc:

Arc length = (central angle / 360) x 2πr

Assuming the radius of the Earth is 6371 km:

Arc length = (284 / 360) x 2 x π x 6371
Arc length = (0.7889) x 2 x π x 6371
Arc length ≈ 9976.75 km

Therefore, the measure of the intercepted arc on Earth is approximately 9976.75 km.