| 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 - 328 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 - 494 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 - 264 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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