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No / ��� t �Sda1 aF a ? TRIGONOMETRIC FORMULYE G I ,1 B B B <br />a <br />a —g a c <br />gidA <br />b C �b C A C <br />.. .. i I Right Triangle - Oblique Triangles <br />-Z7 <br />�T, <br />1 1 <br />Iy ~ <br />©el jell- 0" 16 <br />' .y7 0 0 <br />'1 <br />Solution of Right Triangles - <br />For Angle A. sin = a , cos = c b , tan= a , cot = b , sec = cosec = <br />c b b a. <br />( Given Required ab?'a,b A,B,c tan A=b=cotB,e=Vo,2+bz=a 1 { a <br />`Y as <br />a, c A, B, b sin A =a ic = cos B, b = \/ (c+a) (c—a) = c <br />/ A,a:.="B, b, c B=90'=A,b=acotA,c= a <br />I <br />sin A. <br />i A, b, <br />B, a, c <br />B = 90°—A, a = b tan A, c = b _ <br />_ <br />cos A. <br />A, b r <br />B, it, b I <br />B = 9.02-,A,.a- c in A, b = c cos A, <br />Solution of Oblique Triangles <br />Given <br />Requireda <br />sin B <br />A, B, a <br />b, e, C <br />b _ <br />, C = 180°—(A + B), c = <br />sin A sin A <br />A, a,'b <br />B, c C <br />sin Bb sin A = ,C = 180°—(A (B), c a sin C <br />= <br />a sin A <br />a, b, C <br />A, B, c <br />1 (h—b) tan -'a (A+B) <br />A+B=180 - C, tan z (A—B)= <br />a + b , <br />1 <br />a sin C <br />_ <br />c sin A <br />a, b, c <br />A, B, C <br />s=a+2+c'sin 'A= -VA a(cs-c <br />sin aB=�(s-aa(� ),C=180°—(A+B) <br />a+b-1-c <br />a, b, a <br />Area <br />6= 2 , area = s(s—a s—b)(s—e, <br />A, b, e, <br />Area <br />area = b c sin A <br />2 <br />sin B sin C <br />A, B, C, a <br />Area <br />area - = — <br />2 sin A <br />REDUCTION TO HORIZONTAL <br />Horizontal distance = Slope distance multiplied by the <br />cosine of the vertical angle. Thus: slope distance=319.4ft. <br />Vert. anl= 51 101. From Table, PaIX. cos 10 = <br />e a'StQ�ce <br />y 9959. Horizontal distance=319.4X. 959= 3 3.09 ft.50 <br />sN A Xe <br />a Horizontal distance also=Slone distance minus slope <br />distance (1—cosine With <br />vc <br />times of vertical angle). the <br />distance <br />same figures as in the preceding example, the follow - <br />ing result is obtained. Cosine 50 101=.9959.1—.9959=.0041. <br />,Horizontal <br />i the is known, <br />319.4X.0041=1.31.319.4-1.31=319.09 ft. <br />the horizontal distance is dist- <br />,When rise approximately:—the slope <br />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft., <br />slope distance=3302.6 ft. <br />Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft. <br />2 X 302.6 <br />• MADE IN Y.S.A. <br />I <br />