Stuck on seemingly simple question: Earth-observing satellite

[Astro Kiwi]

I am working on this problem above in my calculus class. Parts b and c gave me no problems, but part a has me stumped. It seems like a simple question to me, but I just cannot seem to get it.

I have tried making sin(theta)=r/h equivalent to h=r(csc(theta)-1), but I keep getting stuck at h=r*csc(theta).

What am I missing? It is probably something simple and obvious. Any help would be greatly appreciated.

 

[Deleted member 4993]

View attachment 8252

I am working on this problem above in my calculus class. Parts b and c gave me no problems, but part a has me stumped. It seems like a simple question to me, but I just cannot seem to get it.

I have tried making sin(theta)=r/h equivalent to h=r(csc(theta)-1), but I keep getting stuck at h=r*csc(theta).

What am I missing? It is probably something simple and obvious. Any help would be greatly appreciated.

You are misinterpreting "h". It is NOT the hypotenuse.

sin(Θ) = r/(r+h) → csc(Θ) = 1 + h/r

 

[Astro Kiwi]

You are misinterpreting "h". It is NOT the hypotenuse.

sin(Θ) = r/(r+h) → csc(Θ) = 1 + h/r

Thanks for the help! That cleared it up. The diagram in the question was not too clear to me.

Got it now.