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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages

## A Complete Epitome of Practical Navigation, and Nautical Astronomy ..., Volume 1

John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...— b : : tan. r (A + B) : tan. X (A - B) 2 2 The above result may be enunciated thus— ^ The sum of two sides is to their difference as the tangent of half the sun of their opposite angles is to the tangent of half their difference. By combining the last two...

## Mathematics for Collegiate Students of Agriculture and General Science

Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...sides arid the included angle are given. 101. Law of Tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of half their difference. From the law of sines, we have a...

## Plane and Spherical Trigonometry

Leonard Magruder Passano - Trigonometry - 1918 - 330 pages
...than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A : sin B....

## Plane and Spherical Trigonometry

Leonard Magruder Passano - Trigonometry - 1918 - 176 pages
...than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposite the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A : sin B....

## Plane and Spherical Trigonometry

Leonard Magruder Passano - Trigonometry - 1918 - 198 pages
...than unity. 54. Case III may be solved by means of the theorem following : In any triangle the sum of two sides is to their difference as the tangent of half the sum of the angles opposlte the two sides is to the tangent of half their difference. Proof : By Art. 51 a : b = sin A...

## Kent's Mechanical Engineers' Handbook, Volume 1

William Kent - Mechanical engineering - 1923 - 1450 pages
...triangle — Theorem 1. The sines of the angles are proportional to the opposite sides. Theorem 2. The sum of any two sides is to their difference as the tangent half the sum of the opposite angles is to the tangent of half their difference. Theorem 3. If from...