 | Webster Wells - Trigonometry - 1896 - 236 pages
...B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ triangle, the sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. By (47), a : b = sin A : sin B. Whence by composition and division, a + b : a — b = sin A + sin B... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...[58] is called the Law of Tangents. Translation : The sum of any two sides of any triangle is to then. difference as the tangent of half the sum of the opposite...angles is to the tangent of half their difference. 101. Relation of the half of one angle to the three sides. For brevity, let a+b + c = 2s; then a +... | |
 | William Kent - Engineering - 1902 - 1204 pages
...The sines of the angles are proportional to the opposite sides. Theorem 8. The sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. Theorem 3. If from any angle of a triangle a perpendicular be drawn to the opposite side or base, the... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...These formulas are derived in Appendix II. 20. Principle of Tangents. — The sum of any two sides of a triangle is to their difference as the tangent of...angles is to the tangent of half their difference. That is (Fig. 6), a + d _ ta a - b ~ tan £(/*-.#) The derivation of this formula is given in Appendix... | |
 | Plane trigonometry - 1906 - 230 pages
...These formulas are derived in Appendix ll. 20. Principle of Tangents. — The sum of any two sides of a triangle is to their difference as the tangent of...angles is to the tangent of half their difference. That is (Fig. 6), ab tan i (A - B) The derivation of this formula is given in Appendix ll1. The student... | |
 | Frederick A. Smith - Hydraulics - 1911 - 242 pages
...tg . 2 2 This means : the sum of two sides in a triangle is to its difference as the tangent of $4 the sum of the opposite angles is to the tangent of half the difference of the opposite angles. This is the second general formula. The third general formula... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. „ „ a sin a: f . ,, Proof. T = - — -, from sine theorem. J b sin j8 ' mi a + b sin a + sin 6... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...logarithms the following theorem is needed: TANGENT THEOREM. In any triangle the sum of any two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. a sina Proof. r = -. — -, from sine theorem. b sin ß m, a + b sin a + sin ß . , . , , Then - т... | |
 | William Charles Brenke - Trigonometry - 1917 - 194 pages
...twice their product by the cosine of their included angle. Law of Tangents. — The sum of two sides is to their difference as the tangent of half the...angles is to the tangent of half their difference. Half Angles. — The sine of half an angle equals the square root of the product of s minus each of... | |
 | William Kent - Mechanical engineering - 1923 - 1450 pages
...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 any angle of a triangle a perpendicular be drawn to IP opposite side or base, the... | |
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In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 
