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TRIGONOMETRIC FORMULAE
<br /> .2 % �a
<br /> z
<br /> B B zyL B
<br /> -- /^7 -
<br /> /� ° a ` a
<br /> Jl t 3
<br /> y� b C tb C 2 2C
<br /> .34 p 2- Right Triangle Oblique Triangles
<br /> q Solution of Right Triangles
<br /> 9'� 1 to - v For Angle A. sin = ,cos= a ,tan= b ,cot = a,sec= h, cosec= a
<br /> 5
<br /> u <{ � �,J rj Given Required a
<br /> 2 2 ! a, b A, B,c tan A= b= cot B,c = as s = a 1 } as `i" !/r-
<br /> A,B, b sin A=a =cos B,b=f\/(c a (o—a =0
<br /> ___._ -— g / Z Z J` ✓ V A,a B, b, c B=90°—A,b =a cot A,c= sin A.
<br /> y/7
<br /> r �� ✓ A, b -B, a, e B=90°—A,a = b tan A,c= cos A.
<br /> ---- C A, e, B,a, b B=90°—A,a=c sin A,b=e cos A,
<br /> y� -Z , �� U , CF /7. / Solution of Oblique Triangles
<br /> ---T 7 GIN en Required a sin$ a ein C
<br /> f --- ./ a `� A B,a b e, C b= , C.= 180°—(A+B), c=
<br /> sin A sin A
<br /> b sin A a sin C
<br /> A, a, b B, c, C sin B= a ,C=.180°—(A+B),c = sin A
<br /> G Z b, C A, B,c A+B-180°—C,tan%(A—B)=(a—b)tan}(A+B)
<br /> a sin C '
<br /> 4 o H sin A
<br /> z{.yam -3 u,
<br /> --- (:r a+b+ i (8_.b)8-0 / 0'8
<br /> ,os r-- , •�_o
<br /> 9 a, b, c A, B, C s= 2 ,sin�A= be
<br /> . 3 S'�
<br /> a) t sin'-,B=�(s—ax8—c ,C=180°—(A�B) '
<br /> _ ac
<br /> a+b+0
<br /> a, b, a Area 8= 2 , area = s(s—a a— (ate
<br /> ,
<br /> [.. 3 9 '
<br /> a .; � A b c Area b e sin A
<br /> area = 2
<br /> L 3 7^ L / as sin B sin C
<br /> _ A,B,C,a Area area = Z
<br /> y 7 _ - 2 sin A
<br /> ✓�• t� 1 S b REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> �J L cosine of the vertical angle.Thus:slope distance=319.Oft
<br /> Vert sng =5°10! From Table,Page IX cos 5°101=
<br /> d9969. H Qontal distanoe=4l9.4X.998=31&09 ft
<br /> ogle R Horizontal distasee also=Slope distance minus slope
<br /> Qe p' distance times(1—cosine of vertical angle). With the
<br /> same Yigares as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 5 1M=.9969.1—.9959=.0041.
<br /> 319c4X.0941=141.3114-1.31=31E_O9 ft
<br /> When the rise is known,the horizontal distance is approximately:—the slope dist-
<br /> ante less the square of the rise divided by twice the slope distance. Thus:rise=14 ft,
<br /> slope distanee=9026 ft Horizontal distance-324—14 X 14=3026-0.22=302.28 ft
<br /> _ 2 X 382.6
<br /> „* t MADE IM U.S.A-
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