The mass, number of moles, concentration or volume of a substance can be calculated easily if you learn two formula triangles.
The basic equation is the sine formula for triangles on a sphere: Fig. 2. Angles α and β between route elements along-track and cross-track and the geographic pole.
Much work then followed, famously similar in each case, in particular to show that in the three-dimensional space described by their assumptions there is a surface upon which Euclidean geometry holds, and to deduce the existence of trigonometrical formulae describing triangles in the plane.
It is, of course, true, that no amount of consistent deductions in the new geometry rules out the possibility that a contradiction does exist, but the intriguing relationship of the new geometry to spherical geometry, and the existence of trigonometric formulae for triangles strongly suggested that the new geometry was at least consistent.
It also, daringly, broke "The Good Wife" 's primal link to a feminine TV narrative formula: the love triangle — the secret sauce for many female fans.
Thus it follows from formula (3.7) and triangle inequality that (3.8).
Now, we will define the same formula for the triangle region : (312).
Now we consider the case 3 ≤ k ≤ N. Applying formula (2.3), the triangle inequality and estimates [46] ∥ A B k C 2 ∥ E → E ≤ M k τ, ∥ B k C ∥ E → E ≤ M, 1 ≤ k ≤ N, (2.7).
The review goes on to state that "for fans of more mainstream romantic productions, it's a neat twist on the traditional love-triangle formula, and a charming alternative to boys meeting girls".
By using the triangle inequality, formula (2.10), estimates (2.9), (2.12), and Lemma 2.2 of paper [15], we obtain ∥ G 1 ∥ H → H = ∥ G ∥ H → H + ∥ G 1 ∥ H → H ∥ G ∥ H → H ≤ M + ∥ G 1 ∥ H → H M M 1 τ. for any small positive parameter τ.
