please help
two questions
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also
A surveillance satellite circles Earht at a height of h miles above the surface. Suppose that d is the distance, in miles, on the sruface of Earth that can be observed fromt eh satellite. See the illustration.
(a) Find an equation that related the central angle theta to the height h
(b) Find an equation that relates the observable distance d and angle theta
(c) Find an equation that related d and h
(d) if d is to be 2500 miles, how high must the stellite orbit above Earth?
(e) If the stellite orbits at a height of 300 miles, what distance d on the surface can be observed?
i bet if i just new how to start these prolbmes i would know how to do the rest
To answer the first question, the provided link appears to be a web address to a specific page on the Jiskha website. You can simply click on the link, and it will take you to the page where you can find the information or question you are looking for.
Regarding the second question about the surveillance satellite, let's go through each part step by step:
(a) We can use trigonometry to determine the relationship between the central angle theta and the height h. The central angle theta is the angle formed at the center of a circle by two radii, one connecting to the observer on the ground and the other to the satellite.
In this case, the observer is located on the surface of the Earth, and the satellite is at a height h above the surface. We can use the inverse tangent function (arctan) to find the relationship between theta and h:
tan(theta) = h / r
where r is the radius of the Earth. Since the radius of the Earth is a constant, we can consider it as a known value.
(b) To relate the observable distance d and angle theta, we can use the arc length formula. The arc length is the distance on the surface of Earth that can be observed from the satellite. The formula for the arc length is:
s = r * theta
where s is the arc length, r is the radius of Earth, and theta is the central angle in radians.
(c) To relate the observable distance d and the height h, we can use the tangent function:
tan(theta) = d / h
(d) If d is to be 2500 miles, we can use the equation from part (c) and substitute the value of d:
tan(theta) = 2500 / h
Rearranging the equation to solve for h:
h = 2500 / tan(theta)
Substituting the known height of the satellite's orbit, you can plug in the value of theta and calculate the value of h.
(e) If the satellite orbits at a height of 300 miles, you can again use the equation from part (c):
tan(theta) = d / 300
Rearranging the equation to solve for d:
d = 300 * tan(theta)
By plugging in the central angle theta, you can calculate the observable distance d on the surface.