...as in 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...

...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...

...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 :...

...10° 12', B = 46°, 36'. Ans. C = 123° 12', 6 = 205.1, c = 236.4. 202 OBLIQUE TRIANGLES 463. THEOREM. 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 sides and the cosine of the included...

...THEOREM 310. 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 upon it. Hypothesis. In A ABC, ZB is acute. Conclusion....

...THEOREM 337. 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 two sides and the projection of the other side upon that one. Given: (?). fc| To Prove...

...Theorem. In any triangle, the square of a side opposite an acute angle is equivalent 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. Fio. 2 Given the triangle ABC, having...

...Theorem. — 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 those sides and the projection of the other upon it. DB Hypothesis. — In A ABC, Z. A is acute,...

...THEOREM 310. 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 upon it. A Hypothesis. In A ABC, ZB is acute. Conclusion....