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TRIGONOMETRIC FORMULIE
<br />B '13
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<br />b G, q b c
<br />L "�'T] Z `* Right Triangle Oblique Triangles
<br />Solution of Right Triangles '
<br />For Angle A. sin = c , toe = ,tan = L ,cot = 2 ,sec = b , cosec c Q
<br />Given Required a 2
<br />a
<br />a,b 1,B,c tanA=b=cotB,c= as F 2=aAI1+-z/
<br />a
<br />lii�,� z
<br />3 -� u `, . ��, _ a•, c A, B, b sin A _ = cos B, b = \/(c+a) (c—a) = o V-1 o a
<br />117
<br />A,a B, b, c B=90'—A,b=acotA,c= sin A.
<br />i A b B, a, c B= 90 —A a= b tan., e,
<br />A= 8
<br />cos A.
<br />A,c B, a, b B=90°—A,a=csin .I,b=ccosA,
<br />Z g Solution of Oblique Triangles �7q v75 rt Given Required a sin B a sin C
<br />-7 o A, B,.((, b, c, G' b = sin A ' C = 180°—(A + B), c = sin A
<br />✓" Z��
<br />Z7 f �� , Vit; 4%� b sin _4 a sin C
<br />t 2 A, a, b R, c, 'C sin B =a C = 180'—(A -;=B), c = sin A
<br />, (a—b)fen J1(A+B)
<br />G
<br />a, b, A, B, c _ I+B=180 — C, tan a (A—B)=
<br />a sin C a b
<br />Ctc=
<br />t,''� / `2,� �% �---• _.�_ - -sin A
<br />a+b+e +-'b)(s-c)
<br />a;, b, c A, B, s= 2 sin 1.4=�� be
<br />G'
<br />4 v •s—c '—(
<br />`0 sin':B=-!! ac
<br />,C=180 .4+8).
<br />a, b, c Area s—a.+2+0,
<br />bcsin A
<br />l ( A, b, c Area area =
<br />� a� •'� i_ b �tet' D y2
<br />A, B, C, a Area area = a" sin B si❑ C
<br />�► '' , r . rb 2 sinA
<br />i. ��c}, �'. ��,j=_- • a' �/ REDUCTION TO HORIZONTAL
<br />y -(-� K �_ Horizontal distance= Slope -distance multiplied by the
<br />`' !�j 1�. c cosineofthe vertical an;tle.Tbus:slope distance =319.4 ft.
<br />~ �'' v Dl .i a's�9pc 89 9. Horizontal distance= 19.4X•99 J =51 101. From Table, e 3 8.09 ft.IX. Cos 5° ld=
<br />)'f'�� `� b� ` e�1oQe ngle = Horizontal distance also=Slope distance minus slope
<br />5�- �' 1' x 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 5° 101=.9959. 1-.9959=.0041.
<br />j
<br />319.4X.0041=1.31-310.4-1.31=318.09 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=l4 ft.,
<br />j.. slope distance=302.6 ft. Ilorizontal distance=303.6- 14 X 14 =3026-0.a2=30228 ft.
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<br />f r MADE IN U.S.A.
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