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TRIGONOMETRIC FORMULIE
<br />. / �/ 9T/4 ui►I gii/etr �B B B
<br />c ° a c a ° a.
<br />fC
<br />A b C A b C A b
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />,
<br />a e
<br />For Angle A. sin b a b c
<br />C' , = cos = c , tan= b , cot = a , sec = b , cosec = a
<br />Given Required
<br />yh� a z
<br />a A,B,c tanA=b=cotB,c= Vla,,+ =a 1 { a
<br />a, c A, B, b sin A a = cos B, b = �/ (c+a) (c --a) = c
<br />c a os
<br />A, a B, b, c B=90°—A, b = a cotA, c— sin A.
<br />Z'Z1' �.
<br />a. A, b B, a, c B =90 —A, a = b tan A, c = coa A. y
<br />CA r % j .+ A, c B, a, b B=90'—A, a = c sin A, b= e cos A, ti, pi
<br />Solution of Oblique Triangles �¢
<br />Given Requiredf
<br />a sin B a sin C y
<br />A, B, a b, c, C b = C = 180°—(A + B), c = L�,s.
<br />sin A ' sin A f, ;
<br />a b sin Aa
<br />a sin C A, a, b B, e, C sin B = a . , C = 180o —(A + B) , c = sin A
<br />�� o o i to—b) tan 3 (A+B)
<br />I3 4,
<br />b, `C d, , c A } B-180
<br />Z — C, tan 2 (A—B)= a + b ,
<br />�3 . 1' y a sin C
<br />c sin A l�
<br />/ 9 247. 9i q9s
<br />a 2 +b+c 1x3;
<br />/ 1 % a, b, c A, B, C S=,sin �A=
<br />� be (za.99S-123,9�
<br />q, j �-Z �t sin 'B=�(s—aa(c c),C=180°—(A+B)
<br />+b+G
<br />a, b, c Area s= ,area
<br />S g7 .37 {\A, b, o Area area = b e sin A
<br />o
<br />a2 cin B sin C
<br />B, C, a. Area area = 2 sin A
<br />y� 22 87 37s \ REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slopedistance=319.4ft.
<br />k l 7 t9rce Vert. angle =5° 101. From Table, Page IX. cos 50 l0'=
<br />. g e ass H 9959. Horizontal distance=319.4X.9959=318.09 ft. 4. g1oQ oa�e a Horizontal distance also=Slone distance minus slope
<br />1D 1 't A 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 50 101=.9959.1—.9959=.0041.
<br />tJ p ✓ �;
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />t/�,�'' _ 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=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2X3026
<br />` i MADE IN V.S.A.
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