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The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.
Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ... - Page 355
by Miles Bland - 1819 - 377 pages

## The British Review, and London Critical Journal, Volume 1

1811
...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...

## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...be found from the tables ; 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...the angle B*. The angle B being found, the angle C= 1 8O - (A + B), and may .-. be determined. Also sin. A : sin. C :: CB : BA, whence BA = CB x •. -...

## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1821 - 544 pages
...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...

## A Popular Exposition of the System of the Universe: With Plates and Tables

Ferdinand Rudolph Hassler - Astronomy - 1826 - 230 pages
...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...

## Elements of analytic trigonometry, plane and spherical

Ferdinand Rudolph Hassler - Trigonometry - 1826 - 192 pages
...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...

## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1832 - 348 pages
...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...

## A syllabus of a course of lectures upon trigonometry, and the application of ...

Henry Pearson - 1833
...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....

## The elements of plane trigonometry, Volume 1

John Charles Snowball - 1837
...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°....

## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson, James Ryan - Surveying - 1839 - 412 pages
...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,...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...^ = — that is, sin. d=sin. (180° — 0) an important proposition which enunciated in words, is, the sine of an angle is equal to the sine of its supplement. Again, cs_cs; CA~CA cos. 6=— cos. (180°— 0), 42 If, as in the annexed figure, we draw CP', making...