 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 diminished by twice the product of one of those sides and the projection of the other upon that side.  A Text-book of Geometry - Page 157by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - Vector analysis - 1901 - 470 pages
...the cosine of the angle between them. Or, the square of one side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the product of either of thpse sides by the projection of the other upon it — the generalized Pythagorean theorem.... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1902 - 186 pages
...circumscribed circle. 41. Law of the cosines. — The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the product of these sides and the cosine of the included angle. Сн. VI, § 41] OBLIQUE TRIANGLES differ slightly... | |
 | Education - 1903 - 630 pages
...equiangular. 6. Prove : 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 diminished by twice the product of one of these sides and the projection of the other side upon it. 7. Prove : The area of a regular polygon... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...THEOREM 659. 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, diminished by twice the product of one of these sides and the projection of the oiher side upon it. b B Let ABC be a A in which BC lies opposite... | |
 | Education - 1903 - 552 pages
...of the opposite angles. (b) Prove that the square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the two sides multiplied by the cosine of their included angle. 10 credits eaeh. 4. The angle of elevation... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...349. In any oblique triangle, tlie square of a 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 those sides by the projection of the other side upon it. ADO Fig. 1 Given acute ZC in A ABC, and DC the projection... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...THEOREM 349. In any oblique triangle, the square of a 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 those sides by the projection of the other side upon it. Given acute ZC in A ABC, and DC the projection of the... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...THEOREM. 375. 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 diminished by twice the product of one of those sides by the projection of the other upon that side. D Fio. 1. Fio. 2. Let C be an acute angle of the triangle... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...THEOREM 373 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, diminished by...one of those sides and the projection of the other side upon it. Fig. 1 Fig. 2 HYPOTHESIS. In the A ABC, the / B is acute, and BD is the projection of... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...THEOREM 373 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, diminished by...one of those sides and the projection of the other side upon it. Fig. 1 Fig. 2 HYPOTHESIS. In the A ABC, the £ B is acute, and BD is the projection of... | |
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