# Math Help - Tricky triogonometri...

1. ## Tricky triogonometri...

How can I find angle v in this figure?

Info:

AO=OB=OP=OC=6370 km

2. Tricky with the figure missing?

3. ## continues....

PS=20240 km
CP = 2780 km

Thanks for all answers

4. Originally Posted by Neffets...:P
PS=20240 km
CP = 2780 km

Thanks for all answers
The key is that $\angle POC=(arcCP)/OC=2780/6370$ radian.

The rest is just fiddly trig.

5. ## thanks

thanks mate! I think i'll manage it all now...

You guys are GREAT!

6. ## need more help...

i have tried a lot, but i have not been able to find the answer!

CP is a part of a circle...
the angle is on a tangent.

Can you guys show me how you find the answer?
I know I seem a bit stupid, but...

7. Originally Posted by Neffets...:P
i have tried a lot, but i have not been able to find the answer!

CP is a part of a circle...
the angle is on a tangent.

Can you guys show me how you find the answer?
I know I seem a bit stupid, but...

Drop a perpendicular from $C$ onto $OS$, call the new point at the foot of the perp. $Q$.

Now look at $\triangle OCQ$ you know $\angle QOC$, and $OC$, so you can find $OQ$ and $CQ$ using the $\sin$ and $\cos$ of $\angle QOC$ and $OC$.

Now switch attention to $\triangle CQS$. You know $SO$ and $OQ$, so you know $QS$. You already know $CQ$, so Pythagoras's theorem will now finish the problem.

RonL

8. Originally Posted by CaptainBlack
Drop a perpendicular from $C$ onto $OS$, call the new point at the foot of the perp. $Q$.

Now look at $\triangle OCQ$ you know $\angle QOC$, and $OC$, so you can find $OQ$ and $CQ$ using the $\sin$ and $\cos$ of $\angle QOC$ and $OC$.

Now switch attention to $\triangle CQS$. You know $SO$ and $OQ$, so you know $QS$. You already know $CQ$, so Pythagoras's theorem will now finish the problem.

RonL
I forgot:

Extent the tangent at $C$ to meet $OS$ at $T$, then $\triangle OCQ$ is similar to $\triangle CQT$. This will allow you to find $\angle CPS$, and you already have enough information to fins $\angle PSC$ which will allow you to find angle at $v$

RonL

9. The attached scan shows all the relevant dimensions and angles filled
in on the diagram.

RonL

10. ## Thanks Captain!

This forum is great! Now I can finally get help when I'm in a tricky situation...
Thanks a lot Captain Black!!!! :-D :-D

I couldn't find the answer with your first explanation, so I'm glad you did remember the rest...

Neffets...:P