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D 3 -
<br /> TRIGONOMETRIC FORMUL& _ T
<br /> B B B
<br /> c
<br /> C c
<br /> a a a
<br /> b C A b C A b C
<br /> Right Triangle Oblique Triangles 1 ��
<br /> Z F
<br /> Solution of Right Triangles - -
<br /> a b a b c 3?s
<br /> For Angle A. sin = o
<br /> 7 ✓' ,cos= ,tan= b;cot = a,sec cosec= a
<br /> a 1 Given Required
<br /> a, b A, B,c tanA=b= cotB,c =1a�-� g = a 1 I �s
<br /> s
<br /> _ � a
<br /> 1 I - as c A, B, b sin A=e =cos B,b= (c+a (c-a) =c 1 eSL
<br /> =
<br /> 1 fl A,a_ B, b, q B=90' b =acot c=
<br /> /J rr _1 stn A. ��
<br /> A, b., B,a, a B=90°-A,a = b tan A,c= -- - •r y,--
<br /> co,s s4.
<br /> A,c B, a, b I B=90°-A,a =c sin A,b=e cos A,
<br /> Solution of Oblique Triangles
<br /> z ;- Given Required
<br /> �✓ ,_. •g A, .B,a b, c, C b=a sin E C= 1800-(A+B) c
<br /> r� sin A sin A
<br /> �. sin C
<br /> A, a, b B, e, C sin B= b sa A,�,= 180°-(A+B),c = ain A
<br /> - s
<br /> s
<br /> a, b, C A,B,c A+B-1801—C,tan 2'(A—B).(a—b)tan (A+B) N
<br /> 5!f ' '� ,✓$� rl � _ � c — a sin C a b
<br /> � r'ppl )L sin
<br /> �� A, B, C s.a+�+c,ein'-sA=��`s
<br /> c '
<br /> z.
<br /> 1 '
<br /> sinB= C=180'-(Af B�)
<br /> as �
<br /> a, b, c Area a=
<br /> a+2+ c
<br /> , area = s(8—a s— )(s—e
<br /> _ A, b, c Area area = besin A
<br /> 2
<br /> A,B,C,a Area area =
<br /> a=sin B sin C
<br /> 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> r cosine of the vertical angle.Thus:slope distance=319.4 ft.
<br /> 1 J 1 ay�tsrce d Vart angle=5°HN. From Table,Page IX.cos b°w= .
<br /> 99 F9 Horizontal distance=319,4X.9959=3l&09 ft
<br /> a�OArg1e a Horizontal distance also=Slope distance minus slope
<br /> „ 4e distance times (1—cosine of vertical angle). With the
<br /> same figares as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 50SW=:)858.1—.9&59=.0041.
<br /> 31&4X.0041=1.31.319.4-1.31=31&09 ft.
<br /> When the rise is known,the horizontal distance is approximately:—the slope dist-
<br /> ance less the square of the rise divided by twice the slope distance. Thus:rise=14 ft..
<br /> slope distanee=3481t. Horizontal distanee=90yg-14 X 14=3016-1132=302.28 ft,
<br /> 2XW16
<br /> MADE IN U.S.A.
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