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<br /> ,.WA;GQNOMETRIC FORMULAE
<br /> B ov B
<br /> a c ally' °`> ° a
<br /> b e C b C A C o
<br /> — oIT 1•L J • �.
<br /> o/ s , xv J Right Triangle Oblique Triangles Z
<br /> . olpttou of Right Triangles
<br /> -- —'
<br /> 7Gu b y
<br /> / u �'"—`� For Angle A. sin a ooe= h tea= a cot =gb sec= cosec/
<br /> ✓ l 9 ng ,. ,
<br /> fy 4 a b a b a
<br /> / ?. (liven Required az
<br /> a, b: A, $„o maA=b= cotB,c = a2+ s = a 1+ as
<br /> 3
<br /> c
<br /> 4-0 f a, c A,B, b sin A m Q=cos B,bc--a) a
<br /> A,-a B, b, a' B=90'—A,b a cotA,o=
<br /> sin
<br /> b 1 "t
<br /> / o c 9 c) 0 3 ,; 2 9 A, b- B,a, o B=90°—A,a = b tan A,c= i f q
<br /> � cos A.
<br /> 7�f A,a B,_a, b B=900—A,a=c sin A,b=c cos A, 8 j o
<br /> 7 G 7 a Solution of Oblique Triangles
<br /> / d Ld 7 f ` l z."-f AGi vena tevul-e b _a sin B� C=180°—(A+B),c =a sin C
<br /> 3 9 J sin A sin A
<br /> A, a, b B a, O sin B= bsin A C= 180 —A B c = asin C
<br /> � /sin A
<br /> z 4a, b, C- .A,-B>4 A+B=180°—C tan 1(A—B) (A-+B)
<br /> a — a—b)tan-a a+ b
<br /> asinC
<br /> _ in A
<br /> rrr
<br /> c =
<br /> +0 1 Iia
<br /> 6 j-�- )a y a, b, a A, B>d s— ,sin'A= ,
<br /> t 6 J ?/ ` �1 1 (s—a)(s—c
<br /> 3-j— a
<br /> L sin B= a c ,C=180 —(A+B)
<br /> a, b, e Areo s - t, area = s(s—a s— )(a—c r 7 z 1
<br /> r, >>
<br /> A, b, o Area, area = b c 2 A
<br /> t G 3 3y J as sin B sin C 7 3 A,B,C,a Area area = j
<br /> 3 p 2 sin.A
<br /> g-7 .v Z 7" REDUCTION TO HORIZONTAL. .
<br /> Horizontal distance=Slope distance multiplied by the
<br /> J .7 cosine of the vertical angle,Thus:slope distance=319..1ft
<br /> Vert. angle=6°101. From Table,Page IX 'cos b°io,=
<br /> o I _d 9959. Horizontal distances=31&4X.9959=31&09 ft.
<br /> 6, 3 g o ( $10 vOt Horizontal distance also—Slope distance minus slope
<br /> j3 3 v 4 a distance times (1—cosine Of vertical angle). With the
<br /> v' .y t same figures as in the preceding example,the follow.
<br /> �( .3 g ' Horizontal distance inirresult is obtained.Cosiee b IN=.9969.1—.9959=.0041.
<br /> 519.4X.4041=L31.319.4—L81tz�318.09 ft.
<br /> 3. U r s ance less t e sqhe uare of a rbe divided by twice the slope the horizontal distance is Odistance.l Thu:rise=14st-
<br /> •7 slope distance=302.8 ft. Horilooutal distance=m28—14 14_�8-0.32=302.28 ft.
<br /> , Z X�30E.8 M
<br /> ,t - MADE IN U.S.A.
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