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<br />TRIGONOMETRIC FORMUL/E Sa
<br />P B B
<br />it
<br />e a c a c a
<br />b CA�b CA
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin = a , cos =b , tan = a , cot = h , sec = cosec =
<br />c c b a b a
<br />Given Required�y 2
<br />a,b 4,B,c tan A=b=cotB,c= 52 2=a 1 I az
<br />c A,;B, b sinA= o =coo B,b02
<br />A, a - i B; b, c B=90°—A, b = a cotA, o= sin A. v
<br />b
<br />A, b"' B,.a, c B=90°—A; a = b tan A, c= cos A.
<br />.A,c '•B,a, b B=90°—A,a=esinA,b=ccosA,
<br />,`
<br />( Solution of -Oblique Triangles -
<br />i Given Required
<br />A, B a ..b : e C b = a sin B , 0 = 180°—(A + B), c = a ein C
<br />sin A sin A
<br />b sin A a sin C
<br />A. B .e C sin B= ,C = 180°— A + B c =
<br />a'':'a ( ), sin A;
<br />(a—b) tan i (A-VAJ
<br />a,'b, 'C;_ A; B, c A+ B=180, —C' tan 7 (A—B)= a + b
<br />e=
<br />a sin C
<br />...tt sin A
<br />i a+b+e �
<br />a, b, o„ A;, C s. 2 ,sin4,A= b c '
<br />sin jB=a c� , C=180°—(A+B)
<br />a-+ b+
<br />a, b, c Area s= 2 , area =V's (s—a s— s—c
<br />Ij A, b, c Area area = b e sin A
<br />A, B, C,a Aras sin• B sin C
<br />ea area = .2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />1 e oe
<br />Vert.
<br />9oangle=
<br />rizontal distance 18.4TableXPage lY_ cos 5° 10
<br />.9959 318.09 ft
<br />959. H
<br />glop A4�1e Horizontal distance also=Slone distance minus slope
<br />Ve distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 10'=.9959.1—.9959=:0041.
<br />319.4X.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 distance=3028 ft Horizontal distance=3028— 14 X 14 =3028—a32=3=8 ft.
<br />w
<br />2X3028 4
<br />- MADE IN U. 8. A.
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