To find the third side a. Sin B sin A :: sin b: sin a. III. Given two angles A and B, and the side c between them. Given two angles A and B, and the side a, opposite to one of them. The other two cases, when the three sides are given to find the angles, or when the three angles are given to find the sides, are resolved by the 29th, (the first of NAPIER's Propositions,) in the same way as in the table already given for the cases of the oblique angled triangle. There is a solution of the case of the three sides being given, which it is often very convenient to use, and which is set down here, though the proposition on which it depends has not been demonstrated, Let a, b, c be the three given sides, to find the angle A, contained between b and c. In like manner, if the three angles, A, B, C are given to find side between A and B. These theorems, on account of the facility with which Logarithm's are applied to them, are the most convenient of any for resolving the two cases to which they refer. When A is a very obtuse angle, the second theorem, which gives the value of the cosine of its half, is to be used; otherwise the first theorem, giving the value of the sine of its half is preferable. The same is to be observed with respect to the side 6, the reason of which was explained, Plane Trig. Schol. END OF SPHERICAL TRIGONOMETRY. |