The figures indicate that the higher the orbit of a satellite, the more of the earth the satellite can "see." Let θ, s, and h be as in the figure, and assume the earth is a sphere of radius 3960 miles.
(a) Express the angle θ as a function of h. (Remember to enter inverse trigonometric functions such as sin–1(x) as either asin(x) or arcsin(x).)
θ (h) =
(b) Express the distance s as a function of θ. (Remember to enter inverse trigonometric functions such as sin–1(x) as either asin(x) or arcsin(x).)
s (θ) =

- anonymous

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- anonymous

figure please.

- anonymous

Let me get a screen shot, really quick.

- anonymous

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## More answers

- anonymous

The radius of the earth is given, 3960 mi.

- anonymous

r -->radius of earth.

- anonymous

Why did you square root the denominator?

- anonymous

Again typo mistake :p
The square root is not present

- anonymous

Ah, okay. That's actually what I got too, when I tried figuring it out now. Do you think you can help me with Part B?

- anonymous

ok
\[s = r \theta = r \cos^{-1} ({r \over r+h}) \]

- anonymous

got it ??

- anonymous

That's for s as function of theta?

- anonymous

\[s = r \theta\]

- anonymous

Got this or I need to explain

- anonymous

Can you explain a little bit? I'm a little confused. Is that for part b?

- anonymous

See I am little confused myself about s. I am assuming that they are taking s as arc length of a circle.

- anonymous

That's what I'm assuming too. But it's really confusing. I agree.

- anonymous

Do you want me to show you how to get s = r (theta) or continue to part C??

- anonymous

Can you show me how s=r(theta), please? Thank you so much.

- anonymous

See we know that
circumference of circle = 2(pi)(r)
If for
2(pi) angle ---> Arc length = 2(pi)(r)
Then
for
(theta) angle --> Arc length = 2(pi) (r) / 2(pi) * (theta)
Therefore Arc length = r * Theta

- anonymous

Oh, okay. I don't know why I couldn't get it in the first place. I was just overthinking it. Thanks! SO MUCH. Can we move on to Part C?

- anonymous

Part C is already done by me. Go above in this thread and check.

- anonymous

Oh! Got it. Got it.

- anonymous

Do you want me to do part d and part e or you will try by yourself??

- anonymous

I'll try by myself first. But can I check with you later to see if i'm correct?

- anonymous

Let me give you a hint because it is 4 am here and I am going to sleep now
Part d) Use s= function of h In this case , h is given. Find s
Part e) s= function of h. In this case , s is given. Find h

- anonymous

Oh, okay. THANK YOU SO MUCH! You saved my life. Haha. Good night!

- anonymous

Welcome :D

- anonymous

If you are having any doubt, post it here and I will see it tomorrow. :)

- anonymous

OK. I'll post what I got from the solving. And you can help me see if I did it right (:

- anonymous

Thank you so much

- anonymous

Welcome :)

- anonymous

Hey, when you get a chance, I computed for the answers. I got d) about 50,462.093 miles; and e) about 0.23 of a mile.

- anonymous

@alinakanus , both the answers are right

- anonymous

@alinakanus , both the answers are right

- anonymous

@alinakanus , both the answers are right

- anonymous

Ah, great! Thank you so much, @shivam_bhalla ! You really helped me a lot!

- anonymous

I apologize for the late response. I was in class up until now.

- anonymous

No problem. No need to apologise !

- anonymous

I still do not fully understand what the answers are after reading it over and over? Starting with A what exactly is the answer?

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