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f. No
<br /> B ic/j• ago c"'Cn G 1 G ✓ "L+� `fi x TRIGONOMETRIC FORMUI-E
<br /> B
<br /> B
<br /> a
<br /> hGu b C b ue C p
<br /> A b C
<br /> 77a
<br /> vv Y h Right Tiiengler Angle A. sin = e
<br /> Oblique Tr'
<br /> ` 4 angles
<br /> 19
<br /> For Solution.o Right Triangles \
<br /> b f
<br /> 6, ,cot = = o
<br /> Given 1te"Ired a'secb. Cosec = a
<br /> ✓ 3 �� . a> b Ar ,c to + a, = a1 aS' 7
<br /> cos B,-a=Vo+a o—ca
<br /> 7
<br /> A, a $ b, o of
<br /> -- - ,b =a cot A.c a
<br /> = Z
<br /> S3 3 stn A. P
<br /> A B
<br /> - , b ;.a, c' = A,a = b tan A,c= b
<br /> cos A.
<br /> f A,c 80 a, b B=9 —A,a=o sin A,b=a cos A,
<br /> • Qlvea Regtttred olution of Oblique Triangles 'f
<br /> _ a sin B
<br /> � 9 3 9 _ B.a b, c, C b sin A ' C= 180°—(A.•�-B), c = a sin C
<br /> b ain A sin A
<br /> !�6 7�' /G 7 'A, a, b B,c, C sin = a ,C— 180°—(A+B),c = a sin C
<br /> 0 S <f y ;In
<br /> A
<br /> b
<br /> a, , C A B e A.+�-'B 80° C,tan%(A—B)— a—b)tan j(4,±jB
<br /> 3r7 a 4 I-Plr aeinC' a+ b
<br /> sin A" CJ
<br /> b, c AA, 2+c,ein JA=�
<br /> 3a r!
<br /> sin g=�l"—ala '&=-180 —(A+B)
<br /> a+b+c
<br /> b, a a 8— 2 , area = s(e—a 8— ) x—G
<br /> �f a
<br /> r]' A. b, c Area area = b c s2 A L o t J y'.7 3
<br /> 7 /. �.
<br /> 71L� S A,B,C,a Area area =
<br /> 2 sin A
<br /> '/7 , REDUCT ON TO HORIZONTAL
<br /> Hzontal distance—Slope distance inultiplIed by the
<br /> cosine of the vert ical angle.Thus:slope distance=319:4 fL
<br /> nista Vert. angle=b 101. From Table,Page IX.cos 50101=
<br /> �oDe 1e 90% Horizontal distance=319.4X.9859=81&09 fL
<br /> Horizontal distance also—Slope distance minus slope
<br /> �e distance times(f—cosine of vertical angle). With the
<br /> (� 4 O 3�7 Z� same figures as in the preceding example,the follow-
<br /> v Horizontal dIsta ing result is obtained.Cosine 5°10'=.9959.1—AM=,0041.
<br /> !t Gn 319.4X.0041=1.31319.4-1.31=31&09.ft.
<br /> v When the rise is known,the horizontal distance-isapproximately:—the slope dist-
<br /> ej
<br /> snee less the square of the rise divided by twice the slope distance. Thus:rise Y4 fL,
<br /> N ,Z ops distance—MB ft. Horizontal distance-302,e—14 14_302.6—M32--302.28
<br /> S 1 2xaxe
<br /> MADE IN U.a,A,
<br /> C
<br /> •
<br /> j
<br /> V s
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