II. Given the two fides b, c, and the angle B opposite to one of them, To find C, and the angle oppofite to the other fide. fin b: finc: : fin B: fin C. Given two angles A and B, and the fide c between them. IV. Given two angles A and B, and the fide a, oppofite to one of them. The other two cafes, when the three fides are given to find the angles, or when the three angles are given to find the fides, are refolved by the 29th, (the firft of NAPIER'S Propofitions), in the fame way as in the table already given for the cases of the oblique angled triangle. There is a folution of the cafe of the three fides being given, which it is often very convenient to use, and which is fet down here, though the propofition on which it depends has not been demonstrated above. Let a, b, c be the three given fides, to find the angle A, contained between b and c. If Rad. 1, and a+b+c=s, In like manner, if the three angles A, B, C are given to find c, the fide between A and B. These theorems, on account of the facility with which Logarithms are applied to them, are the most convenient of any for refolving the two cafes to which they refer. When A is a very obtufe angle, the fecond theorem, which gives the value of the co-fine of its half, is to be ufed; otherwise the first theorem, giving the value of the fine of its half, is preferable. The fame is to be observed with respect to the fide C, the reason of which was explained, Plane Trig. Schol. END OF SPHERICAL TRIGONOMETRY. |