...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...

...constructions. 2. In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it. 3. The areas of two similar triangles...

...XLVIII 195. In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it. Draw A ABC, either acute-angled or...

...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 :...

...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:...

...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...

...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 :...

...trigonometry. V THEOREM 15 The square of the side opposite an acute angle of any triangle equals the sum of the squares of the other two sides minus twice the product of one of the two and the projection of the other upon it. Express as an equation the value of the projection...