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y, 1'✓ TRIGONOMETRIC FORMULAE
<br /> 8✓ B B B
<br /> a e a o a
<br /> bC A�A C A C
<br /> ' //. +¢✓ t Right Triangle Oblique Triangles
<br /> 7� Solution of 12ight Triangles
<br /> 7 For Angle A. sin = o ,toe= ,tan= b ,cot a,ssc= b, cosec= a
<br /> cT;% ^- v Given Required
<br /> a, b A, B,c tan A=b= cot B,c = a%+ z = a 1 + a2
<br /> a, c A, B, b ` sin A=a=.cos B,b=V(c+a) c—a =c 1 T
<br /> 9 1'oJ: 0 1 A,a B, b, c B=90°—A,b=a cot A,o= a
<br /> Iv, CPsin A
<br /> B a, c .B=900-14 a = b tan A,c= b
<br /> 3
<br /> coo A.
<br /> A,c B, a, b I B=90°—A,a=c sin A,b=c cos A, '7
<br /> 9l 70Solution of Oblique Triangles
<br /> d "Required a sin C
<br /> 4j, 'b, c, C b= s nnA , C= 180°—(A+B), o = sin A
<br /> Al b.sin A a sin C
<br /> l3 9 1 rry � b B, c, C sin B= ,0=180°—(A+B),c =
<br /> a sin A
<br /> y ," r E1>B> c A+B=180°—C,tan'(A—B)= a—b)tan-s JA+B)
<br /> a+ b
<br /> ,
<br /> _ asin C
<br /> /2/ c
<br /> sin A ilii
<br /> a+b+o
<br /> b, o A, B,C a= 2 ,sin A_N be )� t;v �� a-a
<br /> 97
<br /> D
<br /> / ti ..r sin 2B=� as a C=180°--(A+B)
<br /> VV
<br /> a, b, c Area a——2 , area = s(a—a a— a—o
<br /> A, b, c Area b o sin A 7 7
<br /> �//( �j .? C y L ti e, area = 2
<br /> [,n /q �'J N / V 7
<br /> I(Ja2:2 a s1II B sin C ,y�c
<br /> �o rc n/e l/c r �C VC/ � Ag V-"d,a7c A,B,Ca Area area = 2 sin A
<br /> 74 6 REDUCTION TO HORIZONTAL
<br /> r ,Tt Horizontal distance=Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus*slope dishmee=319.4 ft.
<br /> _ T
<br /> a Vert- angle=5 1W. From able,Page i oos b°19�=
<br /> h r� 9958. Horizontal distanoe=31$,4X.9968=sl&d9 ft
<br /> 'VU I 5�0 Ap41e Horizontal distance also=Slope distance mi as slope
<br /> G .3 .9 / I G J e distance times<1—cosine of ver ieaT a ). th the
<br /> 4.J same figures as in the preceding esa t e,the follow.
<br /> a Horizontal distance ing result is obtained.Cosine[[°10/=, 0,8969=.0041.
<br /> / $19.4X.9841=1.31.319;6-1.31=3jao9 R
<br /> 1 / - Whenthe rise is known,the}}��orizontal distance is app Lely:-the slope dist-
<br /> / U `3_b risp dialdd6l by Was the dow oe, Thus:rise=l4 ft.,
<br /> ante less the square of the ,
<br /> aS s— slope distance=3028 ft. Horisontat 2X 3D2 9®W� �28&
<br /> S aIN U.a.J6
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