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<br /> 3c' 77 �,t6 •3fJ'q ..
<br /> -� s _ .� _ _� j 3✓ 3 -y TRIGONOMETRIC FORMULAEu�S
<br /> B B B
<br /> A A
<br /> Z b C t O a �.
<br /> Right Triangle Oblique Triangles
<br /> r f Solution of Right Triangles
<br /> a b a b c
<br /> For Angle A. sin =—,con= ,tan= see= ,sec=—, cosec=
<br /> b a b a
<br /> (liven Required a
<br /> a, b A, B,a tan A=b= cot B,c = aY T s a
<br /> a
<br /> a, c A,B, b sin A=c=cos B,b=�/ c-I a) o—a =c
<br /> i
<br /> A a B, b, a B=90°—A b=a cotA c= a
<br /> ay � sin A.
<br /> -� ��� i � � , i- � ►,� A.b B,a, a B=90°—A,a = b tan A,c= b '
<br /> cos A. ?p
<br /> A,a B,a, b I B=90°—A,a=a sin A,b=a Coe A,
<br /> ✓ - / j __
<br /> Solution of Oblique Triangles
<br /> (liven Required
<br /> A!B,a b, a, C b= sin A , C= 180°—(A+B), a =a sin C
<br /> M ., sin
<br /> b sin A
<br /> A, a, b B,6, O sing= a .C= 180°—(A+B),c = sin
<br /> u � .
<br /> V2. a, b, C A,B,'s A+B=180°—C,tan (A—B)� a—b)a+bA--i
<br /> a sin C
<br /> sin A
<br /> 2.Y b a A, B C s_a+b+
<br /> �; fa , , 2 ,sin jA=
<br /> sin aB-�(a-aHa-c C=180°-(A+B)
<br /> ifYX c
<br /> a b as
<br /> _ \ b e Area e_ 1 f
<br /> E d7
<br /> a, 2 ,area = s(a-a s- s--c
<br /> ?`a
<br /> r a 1. ,- / / j" ✓ A, b, c Area area = b c sin A
<br /> 7
<br /> 2 FG. "T•, 3 ua
<br /> f
<br /> A,BCa Area area as sin B sin C
<br /> L
<br /> !_ „ - , , =
<br /> � �• 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Covin.C0t4. 41-;To y° v Horizontal distance-Slope distance multiplied by the
<br /> e cosine of the vertical angle.Thus:slope distance=319.4&
<br /> J `✓° ti-' - StaDoVert. angle-50 101. From Table;Page IX.cos b°id=
<br /> .9969. Horizontal distance=319.4X.9969=31&09 ft.
<br /> // 4 g1pQ �g1e a Horizontal distance also=Slope distance m}nus slope
<br /> Y 4e distance times.0-cosine of vertical angle. With the
<br /> _ \ r
<br /> same
<br /> figures as in the preceding
<br /> ng example,the follow-
<br /> a V ,i N Horizontal distance ng remit is obtained.Cosine b 101=.91-.9968=.004L
<br /> `I �` 318.4X.0041=1.31.319.4-1.31=31&091t.
<br /> L VWhen the rise is known,the horizontal distance is approximately:-the slope dist-
<br /> ane
<br /> (� e less the square of the rise divided by twice the supe distance. Thus:rise=l4 ft.,
<br /> C,, \ slope distance=3028 it Horiaontal distanes=3029-14 X 14=302,6-.==302.28 it,
<br /> 2 X 802.8_ _,,,,. A,
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