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TRIGONOMETRIC FOR__MUL.E
<br />~ Av �� f3'QQ B B B
<br />c c
<br />b b
<br />A k
<br />f G
<br />o-8 y Right',Trianglc } L� Oblique Triangles
<br />t• Solution of Right Triangles
<br />a b a b c c
<br />Z For Angl...4. sin = , cos = , tan= , cot = ,sec = , cosec=
<br />`3 Z �� c c b a b a
<br />Given Required I x
<br />a,b A,B•,c tanA=b=cotB,c=1�a�� =a 1�--
<br />1 a; c -�1, B, b sin A = 6 = cos B, b = � (c+a) (c—a) = c 1 — o a
<br />r x(/`70✓6� I , Y
<br />A, a` B, -b, o B=90°—A, b = a cot A, �a= sin A.
<br />A, b B, a, c B=90°—A, a= b tan A, c= cos A.
<br />A, o. B, a, b B=90°—A,a=csinA,b=ccos A.
<br />Solution of Oblique Triangles
<br />Given Required'
<br />b_ a sin B C= 180,_(A B c= a sin C
<br />s �A, B, a b, C, C sin. A ( + ) sin .A -
<br />a 0'
<br />06( A, a, b B, e, C sin B= b sin A, a = lsa°—(A t B), c = sin'
<br />A
<br />/ur..cC 2.s. S ,+< ° i (a—b) tan '_(A ♦ B)
<br />f.. f , dV3}�1,. a, b, C A, B, c A+B=180 — C, tan , (_i—B)= ,
<br />! i a + b
<br />ao� atsin C
<br />�e L.G `— �• �' C sin ._l.
<br />b, e, A-, B, G g = 2 sin :A= ` b c
<br />sin aB= e�l `—aai'� c),G'=180°—(A } .BJ
<br />�T :+ .
<br />a-{- b -{- c
<br />a a, b, c- --A'f a : s= 2 ,arca = /s(s—a) s—b) (s—c)
<br />br,sinA O
<br />�CZ�-`�U�-!�, _�_ l+. A_ b, iry _l ; °!' area = 2 � p �-
<br />�� O
<br />• :�l� A, B, C,`a Area area a^ s2 s A in B sin C
<br />�. - l•E +SUCTION TO HORIZONTAL
<br />O; Horizontal distance=Slopedistance multiplied by the
<br />cosineoftheverticalangle.Thus: slope distance =319.4 ft.
<br />tao°e Vert. angle=5° 10'. From Table. Page I%. cos 5'101=
<br />61 a atis 9959. Horizontal distance=319.4X.995J=313.08 ft.
<br />Horizoc5_o�ett distance timest(.lcco ine oflvertical angle).ope distance 1With ntis lthe
<br />v same, figures as in the preceding example, the follow-
<br />-. Y — ,:?—_� • + Horizontal distance f ing result is obtained. Gcsine 5°10'=.999.1—.9959=.0041.
<br />319-4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />�p ` $ 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=303.8 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2' X 302:6
<br />MAGE IN U.
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