...c, can be derived in like manner, or can be obtained from (1) by symmetry, viz. : In words: In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine...

...perpendiculars from A and B we get b2 = a2 + c2 - 2 ac cos B. c2 = a2 + b2 - 2 ab cos C. LAW OF COSINES. In any triangle the square of any side is equal to the sum of the squares of the other two sides less twice the product of these two sides and the cosine of the included...

...notation: a sin A b sin B' (2) The "Law of Cosines."—The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included angle: a 2 = b 2 -fc 2 — 26c cos A, with two analogous formulae obtained by "advancing...

...B ' with two analogous formulas obtained by "advancing the letters." (2) The "Law of Cosines." — The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included 'angle:...

...sin A with two analogous formulae obtained by "advancing the letters." (2) The "Law of Cosines." — The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included angle :...

...the case considered above. This result, called the law of cosines, may be stated as follows : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice their product into the cosine of their included angle. Example...

..."advancing the letters." (2) The "Law of Cosines." — The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included angle : a* = b2 + c2 — 26c cos A, with two analogous formula obtained by "advancing...

...in all cases. THE LAW OF COSINES. The square of any side .of a plane triangle is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle. This may be regarded as a generalization of the Pythagorean Theorem to which it...

...angle opposite the other side ; in the usual notation : a sin A b sin B ' (2) The "Law of Cosines." — The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included angle :...

...B ' with two analogous formulas obtained by "advancing the letters." (2) The "Law of Cosines." — The square of any side is equal to the sum of the squares of the other two sides, minus twice their product times the cosine of the included angle :...