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<br />TRIGONOMETRIC FORMULtE
<br />LrB •v d C
<br />07-Q ,. ,� ;� Right.Triangle 'I-- I��• Oblique Triangles
<br />Solution'of Right Triangles
<br />' a, b a b c a
<br />` For Angle A. sib =-`a ,cos = , tsn =b , cot =, a ,sec.= b , cosec = a
<br />i c
<br />Given' 'Required a Y
<br />�'. •(� - -' �} j a, b A, B ,6 tan A = - = cot B, c = a + z = a 1 + --
<br />p I b a2
<br />Vj
<br />A> B, b sin A = c = cos B, b = \l(i+a)
<br />A, -o: - :'.B, b, c` a
<br />�✓ � 1J u•• B=90°—A,b=acot A,c=
<br />sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, c B, a, b B = 90°
<br />f —A, a = c sin A, b= c cos A,
<br />}' J 7 L Solution of Oblique Triangles
<br />�C C',. x. Given Required a sin B
<br />_
<br />� - �_ r, - 4, S A, B, a b, c, C b :- , C = 180°—(A -}- B), a = a sin C
<br />sin A sin A
<br />b sin A a sin C
<br />r - ,� � jj
<br />} A, _a, b B, c,. C sin B = a , C = 1'80 (d } B) , c =
<br />to I„-. N.. � - , � . ,� sin A
<br />Q M` Q� � 6 % a, b, C A, B, c A+B=180°— C, tan z (A—B)= (a—b) tan (A+B)
<br />a '
<br />a, _ _asin C
<br />tj t a sin A
<br />? i%lel� a, b, a A, B, C s= 2 a+b+0,sin'-A= As (s0)
<br />�( ' be '
<br />t" ZJI siniB=N(s a(� ),C'=180°-{A+B)
<br />�•) d �'a+b+c
<br />a, b, c Area
<br />V . s= 2 ,area s— (s—c
<br />G ty
<br />q D 2 A, b, c Area area = b c sA �? 3 %
<br />1 A, B, C, a Area as sin B sin
<br />area = 2 sin A
<br />t
<br />1-
<br />%0��, REDUCTION TO HORIZONTAL'
<br />Horizontal distance = Slope distance multiplied by the Z cosine of the vertical angle. Thus: slopedistance =319.4ft.
<br />a�s11er Vert. angle= 51 101. From Table, Page IX. cos 51 10!=
<br />e 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />H
<br />- glop Angle a Horizontal distance also= Slope distance minus slope
<br />4 p Ve distance times (1—cosi4e of vertical angle). With the
<br />samefigures as in the preceding example, the follow-
<br />j 67 Horizontal distance ing result is obtained. Cosine 5'101=.9959.l—.9959=.004l.
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />al
<br />ist- '
<br />aace less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft.,
<br />�vb 14X14—
<br />�7 slope distance=302.6 ft. Horizontal distance=3026— =302:6-0.32=30228 ft.
<br />2 X 302.6
<br />�1 �"' MADE IN U. 8. A.
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