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.
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
1 answer