Rorschach
- 10
- 0
Consider the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$ and $P_3 = (1/\sqrt{3}, 1/\sqrt{3},1/\sqrt{3})$. Find the angles $\phi_1, \phi_2, \phi_3$ of $\mathcal{P}$ at $P_1, P_2, P_3$ respectively.
I know the cosine angles are $\cos(\theta_1) = 0$, $\cos(\theta_2) = \cos(\theta_3) = 1/{\sqrt{3}}$. I know the cosine formula is $\cos{c} = \cos{a}\cos{b}+\sin{a}\sin{b}\cos{C}.$ However, I can't put these ideas together to find the angles. Could someone please show me how to do that? Thanks.
I know the cosine angles are $\cos(\theta_1) = 0$, $\cos(\theta_2) = \cos(\theta_3) = 1/{\sqrt{3}}$. I know the cosine formula is $\cos{c} = \cos{a}\cos{b}+\sin{a}\sin{b}\cos{C}.$ However, I can't put these ideas together to find the angles. Could someone please show me how to do that? Thanks.