Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 32
... chapter ; and the remaining angles either by a repetition of the same rule , or by the relation of sides to the sines of their opposite angles . Example I. 11. The three sides of a triangle are 32 Plane Trigonometry .
... chapter ; and the remaining angles either by a repetition of the same rule , or by the relation of sides to the sines of their opposite angles . Example I. 11. The three sides of a triangle are 32 Plane Trigonometry .
Página 33
... Example I. 11. The three sides of a triangle are 40 , 34 , and 25 . Required the angles . By Rule I. - BC : AD- - BD ; AS AB : AC + BC :: AC 59 × 9 that is , 40 : 59 :: 9 : = 13.275 . 40 40+ 13.275 Then = 26.6375 = AD : A D B 40-13.275 ...
... Example I. 11. The three sides of a triangle are 40 , 34 , and 25 . Required the angles . By Rule I. - BC : AD- - BD ; AS AB : AC + BC :: AC 59 × 9 that is , 40 : 59 :: 9 : = 13.275 . 40 40+ 13.275 Then = 26.6375 = AD : A D B 40-13.275 ...
Página 34
... example falls : and it will then be found , since a right angle is always one of the data , that the rule usually becomes simplified in its ap- plication ; as appeared in the solution of the second ex- ample to case 2 . 2. When two of ...
... example falls : and it will then be found , since a right angle is always one of the data , that the rule usually becomes simplified in its ap- plication ; as appeared in the solution of the second ex- ample to case 2 . 2. When two of ...
Página 35
... Example I. 14. In a right angled triangle are given , the hypo- . thenuse and the base , 25 and 24 respectively ; to find the rest . Perp . ( hyp.2 - base2 ) = √ ( 25 + 24 ) . ( 25-24 ) = 7 , perp . base 7 1.75 24 = = ' 2916666 = tan ...
... Example I. 14. In a right angled triangle are given , the hypo- . thenuse and the base , 25 and 24 respectively ; to find the rest . Perp . ( hyp.2 - base2 ) = √ ( 25 + 24 ) . ( 25-24 ) = 7 , perp . base 7 1.75 24 = = ' 2916666 = tan ...
Página 46
... example , A 60 ° , then cos a = sin 30 ° = 1 , and cos 30 ° √ ( 2 + 1 ) = { √3 = · 8660254 , sin 30 ° ( 2-1 ) , as it ought to be : cos 15 ° = √ ( 2 + √3 ) = { { √6 + √2 ) = • 9659258 sin 15 = √ ( 2 √3 ) = 1 ( √ / 6 = / 2 ) ...
... example , A 60 ° , then cos a = sin 30 ° = 1 , and cos 30 ° √ ( 2 + 1 ) = { √3 = · 8660254 , sin 30 ° ( 2-1 ) , as it ought to be : cos 15 ° = √ ( 2 + √3 ) = { { √6 + √2 ) = • 9659258 sin 15 = √ ( 2 √3 ) = 1 ( √ / 6 = / 2 ) ...
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altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith