 The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.  Plane and Spherical Trigonometry - Page 52by George Albert Wentworth - 1882 - 201 pagesFull view - About this book
 | William Chauvenet - 1852 - 268 pages
...written a — (22°) v J and we may infer the same relation between 4, c, J?, C and a, c, A, C. 119. The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...Sin. В °r' с ~ Sin. C' ie, b : с : : Sin. В : Sin. C, (A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...Sin. В ог' с - ЖГс' ie, b : с :: Sin. В : Sin. С, (А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...A-\- sin B : sin ^4 — sin B : : .-. a-\-b : a — b : : tan \(A-}-B) : tan %(A — B). 97. Theorem. The square of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Aaron Schuyler - Measurement - 1864 - 512 pages
...tan£(^+Б) : tan\(AB). ... a + b : a — b : : tan \(A+B) : tan %(A— B). 97. Theorem. The sqmre of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...A-\- sin B : sin A — sin В : : . • . a + 6 : a — b : : tan — B). •' tan K^~ -0)97. Theorem. The square of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Henry Nathan Wheeler - 1876 - 128 pages
...tangent of half the sum of the opposite angles is to the tangent of half their difference . . 73 § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their... | |
 | Harvard University - 1876 - 554 pages
...of halt' the sum of the opposite angles is to the tangent of half their difference. 10. Prove that the square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the... | |
 | Henry Nathan Wheeler - Trigonometry - 1876 - 218 pages
...— 6- sin A - sin B In like manner , [6 ' _ , a — c taiVfCA — C)' b — c tan£(B — C), § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice (he product of those sides into the cosine of their... | |
 | Henry Nathan Wheeler - Trigonometry - 1882 - 244 pages
...— B) Тч , L°°J a^c ~ tan l (Ä^ b4-c_tan|(BlC) ' a"C b — с ~ tw! | (B — C)1 § 73. 27ге square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their... | |
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