...have Sin. A. Cos. B + Cos. A. Sin. B — t- ' and Sin.c = Sin.(180* — A + B) = Sin. A + B, since the sine of an angle is equal to the sine of its supplement. Hence Sin. A + B = Sin. A. Cos. B 4- Cos. A. Sin. BQED All this is perfectly legitimate ; but how is...

...and (78) A e CB : CA :: sin. A : sin. B•, CA hence sin. B = ~ x sin. A, and may .-. be determined. But as the sine of an angle is equal to the sine of its supplement, the angle B may be greater or less than a right angle, unless BC be greater than AC and consequently...

...(78) xc CB : CA :: sin. A : sin. JB; CA hence sin. U = „-£ x sin. ^/, and may .'. be determined. But as the sine of an angle is equal to the sine of its supplement, the angle B may be greater or less than a right angle, unless BC be greater than AC and consequently...

...when the given angle is acute and opposite the lesser of the given sides, the answer is ambiguous, as the sine of an angle is equal to the .sine of its supplement, consequently the required angle opposite that other given side may be obtuse, or acute ; unless it...

...No. 1, of the series A, or first definition, we have in the two triangles, and in both cases, (since the sine of an angle is equal to the sine of its supplement.) dd — = sin C ; and — = sin B bc Therefore : d = b . sin C = c . sin B Or, expressed in a proportion...

...No. l, of the series A, or first definition, we have in the two triangles, and in both cases, (since the sine of an angle is equal to the sine of its supplement.) dd — = sin С ; and — = sin В b Therefore : d = i . sin С = с . ein B Or, expressed in a proportion...

...but when the given angle is acute, and opposite the less of the given sides,the answer is ambiguous, as the sine of an angle is equal to the sine of its supplement, consequently the required angle opposite that other given side may be obtuse or acute, unless if is...

...angle is equal to the sine of its complement. C 7. Sin (TT - 9) = sin 9, cos (TT - 9) = - cos Q. Or the sine of an angle is equal to the sine of its supplement, and the cosine of an angle is equal to the cosine of its supplement, with its algebraical sign changed....

...determine B from (ii), С and с are known from (i) and (iii), and the triangle is determined. Now the sine of an angle is equal to the sine of its supplement, and therefore there are two angles which satisfy (ii), the one greater and the other less than 90°....

...but when the given angle is acute, and opposite the less of the given sides, the answer is ambiguous, as the sine of an angle is equal to the sine of ita supplement, consequently the required angle opposite that other given side may be obtuse or acute,...