The furthest this is satellite City can directly reach in the length of the segment tension to the curve of the Earth's surface the diagram is not drawing the scale if the angle form by the tangent satellite signal is 128 degrees what is the measure of the intercepted arc on Earth
A 52
B.104
C.128
D.64
Without any specific measurements given, we can assume that the diagram is not drawn to scale and solve using variables.
Let's call the radius of the Earth "r", and the length of the segment connecting the satellite and the Earth's surface "x". We want to find the intercepted arc on the Earth, which we can call "y".
Using trigonometry, we can say that:
sin(128) = r / (r + x)
Solving for x, we get:
x = r * (1 / sin(128) - 1)
To find y, we need to use the formula:
y = 2 * r * sin(θ/2)
Where θ is the angle intercepted by the arc on the Earth. We know that the tangent to the satellite signal makes an angle of 128 degrees with the segment connecting the satellite and Earth's surface, so the angle intercepted by the arc on the Earth is:
180 - 128 = 52 degrees
Plugging in the values, we get:
y = 2 * r * sin(52/2)
y ≈ 104
Therefore, the answer is (B) 104.
To find the measure of the intercepted arc on Earth, we need to use the information given, which includes the angle formed by the tangent satellite signal.
Based on the information given, the angle formed by the tangent satellite signal is 128 degrees. This angle is formed by the tangent line (representing the segment tension) and the line from the tangent point to the center of the Earth.
Since the total measure of a circle is 360 degrees, and the angle formed by the tangent signal is 128 degrees, the intercepted arc can be calculated by subtracting the angle from the total measure of the circle.
So, the measure of the intercepted arc on Earth is 360 - 128 = 232 degrees.
Therefore, the correct answer is not provided in the options given.