 | 1892 - 724 pàgines
...not found in this line of study one example involving the relation of cause and effect. We may say of any triangle, "The sides are proportional to the sines of the opposite angles," but we cannot properly say any part of a triangle is the cause of any other part. Whoever can speak... | |
 | Edward Albert Bowser - 1892 - 392 pàgines
...following : 1. tan B = cot A + cos C. 2. sin2A = sin2B. W -o? OBLIQUE TRIANGLES. 95. Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB. We have, then, in both figures CD «= a sin B... | |
 | Edward Albert Bowser - 1892 - 194 pàgines
...— (г 7. tan2A = 2 ab V - a1' 8. sin3A = c2 S ab2 -a3 OBLIQUE TRIANGLES. 55. Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles. Let ABC be any triangle. Draw CD perpendicular to AB. We have, then, in both figures CD = a sin В... | |
 | Ernest William Hobson, Charles Minshall Jessop - 1892 - 328 pàgines
...its sine is I, determine cos ^- by means of the expression (/3) of the last question. 5. Show that in any triangle the sides are proportional to the sines of the opposite angles. 6. If a straight line be drawn bisecting the angle A of a triangle ABC to meet the opposite side in... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - 1893 - 434 pàgines
...tany tana + tanatan/3 = l. CHAPTER XIII. RELATIONS BETWEEN THE SIDES AND ANGLES OF A TRIANGLE. 137. In any triangle the sides are proportional to the sines of the opposite angles; that is, ab _ c sin A sin B sin G' (1) Let the triangle AEG be acute-angled. From A draw AD perpendicular to... | |
 | William Wade Fitzherbert Pullen - 1896 - 344 pàgines
...the triangle of forces XYZ, the angle the angle and the angle Z = C + D. XlC, And further, because in any triangle the sides are proportional to the sines of the opposite angles, then H Fs1 ~Y sin Z sin X and putting in the equivalents of the angles, we have HT? 1 1? 1 ri • r<>... | |
 | Frederick Anderegg, Edward Drake Roe - 1896 - 136 pàgines
...the angles opposite these sides by A, B, C, respectively. a. Theorem of Sines. § 65. In any plane triangle the sides are proportional to the sines of the opposite angles. Let ABC represent any plane triangle. Let p represent a perpendicular let fall from any vertex upon... | |
 | 1897 - 726 pàgines
...Solution of oblique triangles. The relation of the three angles of a triangle. The sides of a triangle are proportional to the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle is to their difference as the tangent of half... | |
 | 1899 - 824 pàgines
...expressions for all the values of a, cosai (1 — Cos Í) = sin2!» (1 + cos <). 0) (2) 5. Prove that in any triangle the sides are proportional to the sines of the opposite angles. If in a triangle ABC perpendiculars are drawn from the vertices to the opposite sides, show that the... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 184 pàgines
...considered. For the general form of these theorems and their proof, see Art. 43. 40. Law of the sines. — In any triangle, the sides are proportional to the sines of the opposite angles. In either Fig. 52 (a) or 52 (5), let the length of the perpendicular DO be represented by h. Then in... | |
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Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
