 | Geometry, Plane - 1911 - 192 pages
...Prove that in any plane 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 by the projection of the other side upon it. Show what this theorem becomes when one of these latter... | |
 | Daniel Alexander Murray - Plane trigonometry - 1911 - 158 pages
...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 of their included angle. Relation (1) may be expressed as... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other side upon it. Ex. 726. If the sides of a triangle are 7, "8, and 10, is the angle opposite 10 obtuse, right, or acute... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it. Given in A abc, p the projection of b upon c, and the angle opposite a obtuse. To prove a2 = 62 + c2... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 330 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it. Given in A abc, p the projection of b upon c, and the angle opposite a obtuse. To prove a 2 = ft 2... | |
 | George Clinton Shutts - Geometry - 1913 - 496 pages
...theorem may be stated in general as follows: The square of any side of a triangle equals 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. NUMERAL RELATIONS C, MA Given a A with sides a,... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 272 pages
...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... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 254 pages
...formulate the law. 110. Law of Cosines. In any plane triangle, the square of any side equals the sum of the squares of the other two sides, minus twice the product of the two into (times') the cosine of their included angle. CASE I. The Square of a Side Opposite an... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 pages
...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...sides and the projection of the other side upon it. Fio. 2 Given the triangle ABC, having an acute angle C, and d the projection of a upon AC. •„ To... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...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...one of these sides and the projection of the other upon it. Hypothesis. In A ABC, ZB is acute. Conclusion. 62 = a2 + c2 — 2 a • p°. Proof. 1. Draw... | |
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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. 
