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IV
<br />OA _ TRIGONOMETRIC FORMUL&
<br />COS _ ,.-,b„ ,� B s
<br />4
<br />�, z 9
<br />3 c a c a c a 7
<br />mos _� J A�1 a
<br />o G� s'3 s a aga.
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<br />DD g0 9 i Right Triangle Oblique Triangles t ? —`
<br />Solution of Right Triangles �� 0
<br />'4 For, Angle d: sin = �;, cos = ,tan = b, : cot = a ,sec. b , cosec = a Z
<br />= .(liven Required
<br />�� Ste- C. --- i •� _ i (� '1 , , b d, B ,c tan A — b — cot B, c = a 17
<br />�n�� a,c A,B,b sin A, B
<br />6=coa,b=4�^:
<br />�l o
<br />)a p X G Q Si A, a B, b, e B = 90°—A. b = a cot, asin A.
<br />Z0 i1 c A, b B, a, e B = 90°—A. a = b tan A, c — cos A. �' Z
<br />d, c B, a,, b B = 90°—A, a = c sin A, b = c cos 6.,
<br />Solution of. Oblique Triangles
<br />23 —i Given Required a sin B asin a '�?- Z_7
<br />3 0«3 z 7 yti r. �, B, a b, c, C b sin A , C.= 180°—(� ) B). c = sin '
<br />• Q 3;Z 7 . 110. b sin A a sin,
<br />'
<br />D-----*_^_" �(P ,A, a b B c C sin B , C= 180°—(A + B). c=
<br />333 8 9 7 8 a sin +
<br />o— 1 (a—b) tan i (� { B)% -e_
<br />1 ;a, b, a d, B, c FB -180 a, tan ; (d -B)= y�
<br />Tr%�a —
<br />asinC a + b
<br />sin A, a o
<br />7 / .�` a+b -} o f . c: Z
<br />a, b, a A, B, a ' s = ,sin sd= ..
<br />S 2 �- be
<br />D �I sin zB—
<br />o a b e 1 ac
<br />a;, b; e, Area 4— +2+ , area = a(,,—a s— )(s—c
<br />ba sin A, `-za•�%_
<br />A, b, c Area area = 2 , n 7.-
<br />�% �Z3 a'sin Bsin a N
<br />(y {r} G;A; B, C, a Area , area = f 4 - 7 6
<br />2 sin .A
<br />pej"5" REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied bythe• `
<br />cosine of the vertical angle. Thus: slope distJX cos
<br />ance =319.4 ft.�{�, %
<br />a a�starce y 9959. aHorizontal distance=319.4X..99;= 51 101. From Table, 9 3 &09 ft. 5o IO
<br />- Horizontal distance also=Slone distance minus slope
<br />-7 s 5 Ari a distance times (1—cosine of vertical angle). With the
<br />f I qe same figures as in the preceding example, the follow-
<br />ing result is obtained Cosine 5° 101=.9959.1-9959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximate]?:—the slope dist-
<br />: s )f ante less the square of the rise divided by twice the slope distance. Tbus: rise=l4 ft.,
<br />S=
<br />' �• q `' ': � �" �
<br />slope distance=3026 ft. Horizontal distance=3026— 14X1430Z.6--X0.32=302.28 ft.
<br />n� 2 X 302.6
<br />•� ) i !. - MADE aN Y.B. M
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