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<br />TRIGONOMETRIC FORMULfE
<br />J6 �'�%� S_� - `. I3 B B
<br />_ I
<br />a
<br />1 303��
<br />c a - c a
<br />Y i 9 J,_ ,t -` ., �. CI d b G' A b C
<br />T RightNriangle. Oblique Triangles
<br />Solution of Right Triangles
<br />L �u a b a b c c
<br />r (/ For An ic'A. sin = — , cos = , tan= b , cot = , sec = b , cosec =
<br />�':' { g —
<br />1.� Given Required c a Z 2 a
<br />a, b A, B ,c - tan A = — = cot B, c = a2
<br />{ ra 6 $ a
<br />A, B, b sinA= = — =cos B, b = �/ (c-�(L)-(c—a•) = C 1— 9
<br />%. y ,�-
<br />,;.r 1' � o y � :a � .
<br />L�Y A,a B, b, c B=90°—A, b.= acotA,ca y
<br />�� V �� � . •- • sin�A,
<br />� 5; 7 �� _,' �' A, b B, a; e B=90°—d,a = btan_4,c=
<br />Q _/ cos A.
<br />� ✓ i�'r "' 9•9 7" 7' < i6 T c! A,c' B,a, b' =90°—,a*=asinAbA
<br />,=ccos, �� 1•Ggi.il rY
<br />I; h G ' BA`P
<br />_ � . o tit, 0 !� _ I Solution of Oblique Triangles
<br />/ Given Required
<br />_ a sin .B r_ y ° a sin C
<br />` A' B' a. I b' �'. C .b sin A , G 80 —(d T B), c = sin A
<br />21,f b sin A a sin C
<br />r_% A,a,b I3,o,C sing= a ,C=180°—(-4 (I3)rc= sinA_�%
<br />3ti
<br />r
<br />r • - f?�. v a, b, C A, B, c A+B=180 — G, tan (A—B)— a—b tan - A B
<br />a.� 6 k — a sin C
<br />sin.A
<br />�e. 't_ —_ c -� r.• l i%Y ¢, b, c A, B, C s-a+2+c sin .9=`lt` plc—a)
<br />sin'B=� a(•c
<br />B
<br />c)' a�
<br />{ 2 80. -(� )
<br />a; b, c Area s= 2 ,area = s(s—a = �)'(s—c)
<br />b
<br />/��
<br />�' %y ; , b; c Area area = b
<br />� A
<br />C sin A
<br />2 F
<br />AB, C, a? sin B sin C
<br />, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />4 /x cosine of the vertical angle. Thus: slope distance=319.4 ft.
<br />`3 a%S�Q�ce 0 .99 9. Horiizontal distance 19.4TableX. 959=3 8.09 ft.Ix. Cos 1(Y
<br />! 1. %%ope �bg1c i~ Horizontal distance also=Slope distance minus slope
<br />4V; ��- I; yet. distance times (1—cosine of vertical angle). With the
<br />k� - —_-� same figures as in the preceding example, the follow-
<br />�. S�' ' " `gg• Horizonial distance ing result is obtained. Cosine 30101=.9959.1—.9959=.0041.
<br />319.4X.0011=1.31. 319.4-1.31=31&09 ft.
<br />1 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 distance=302.6 ft. Horizontal distance=302.6— 14 X 14•=302.6-0.32=302.28 it.
<br />2 X 303 6
<br />' - - MADE IN U.S.A.
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