First, we need to use the fact that the angle formed by the tangent satellite signals is 104 degrees to find the central angle (θ) of the intercepted arc on Earth:
θ = 180 - 104 = 76 degrees
Next, we use the formula for calculating the length of an arc:
length of arc = (θ/360) x 2πr
where r is the radius of the Earth.
Since we want to find the length of the intercepted arc (x), we can set up the following equation:
x = (θ/360) x 2πr
We know that the radius of the Earth is approximately 6,371 kilometers, so we can substitute that value in and simplify:
x = (76/360) x 2π(6,371)
x = (0.2111) x 40,075.16
x ≈ 8,470 kilometers
Therefore, the measure of the intercepted arc (x) on Earth is approximately 8,470 kilometers.
The farthest distance a satellite signal can directly reach is the length of the tangent to the curve of Earth's surface. If the angle formed by the tangent satellite signals is 104°, what is the measure of the intercepted arc (x) on Earth?
Hint: If minor arc AC = x then remember that major arc ABC = 360 - x. You will need to substitute into your equation provided in the theorem.
Show all work.
(This is 10th grade math, please don't make it advanced, shorten the steps.)
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