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 28
... found less liable to produce error than that in which the arith . comp . is put down at once from the tables . Example II . 5. In a plane triangle ABC are given AC = 216 ; CB 117 ; the angle A 22 ° 37 ′ ; to find the rest . Construction ...
... found less liable to produce error than that in which the arith . comp . is put down at once from the tables . Example II . 5. In a plane triangle ABC are given AC = 216 ; CB 117 ; the angle A 22 ° 37 ′ ; to find the rest . Construction ...
Página 32
... find the rest . Ans . Angles 33 ° 35 ' , 18 ° 21 ' , side 2400 . CASE III . 10. When the three sides of a plane triangle are given , to find the angles . 1st Method . Assume the longest of the three sides as base , then say ...
... find the rest . Ans . Angles 33 ° 35 ' , 18 ° 21 ' , side 2400 . CASE III . 10. When the three sides of a plane triangle are given , to find the angles . 1st Method . Assume the longest of the three sides as base , then say ...
Página 35
... find the rest . Perp . ( hyp.2 - base2 ) = √ ( 25 + 24 ) . ( 25-24 ) = 7 , perp . base 7 1.75 24 = = ' 2916666 = tan 16 ° 15 ′ 37 ′′ , angle 6 - at the base ; whence 90 ° — 16 ° 15 ′ 37 ′′ = 73 ° 44 ′ 23 ′′ , ́ angle at vertex . base ...
... find the rest . Perp . ( hyp.2 - base2 ) = √ ( 25 + 24 ) . ( 25-24 ) = 7 , perp . base 7 1.75 24 = = ' 2916666 = tan 16 ° 15 ′ 37 ′′ , angle 6 - at the base ; whence 90 ° — 16 ° 15 ′ 37 ′′ = 73 ° 44 ′ 23 ′′ , ́ angle at vertex . base ...
Página 36
... find the other leg and the hypothenuse . Ans . Leg 280 , hypothenuse 480 . Ex . 3. In a right angled triangle are given the base 195 , its adjacent angle 47 ° 55 ' ; to find the rest . Ans . Perp . 216 , hyp . 291 , vert . ang . 42 ° 5 ...
... find the other leg and the hypothenuse . Ans . Leg 280 , hypothenuse 480 . Ex . 3. In a right angled triangle are given the base 195 , its adjacent angle 47 ° 55 ' ; to find the rest . Ans . Perp . 216 , hyp . 291 , vert . ang . 42 ° 5 ...
Página 87
... determine to which the result belongs . Case II . 27. Given the hypothenuse a , and one of the sides ; to find the rest . sin B = COS C = sin b sin a cos a cos b ; or , sin angle req . = ; or , cos side req . = cos c tan b cot a ; sin ...
... determine to which the result belongs . Case II . 27. Given the hypothenuse a , and one of the sides ; to find the rest . sin B = COS C = sin b sin a cos a cos b ; or , sin angle req . = ; or , cos side req . = cos c tan b cot a ; sin ...
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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