|
J TRIGONOMETRIC FORMUL F,
<br /> B t(, 1 B B
<br /> _ � 1 py.SSS - �(
<br /> Right Triangle Oblique Triangles
<br /> /0-5 78 11 D,z '- _ '^� La Solution of Right Triangles
<br /> For Angle A. sin =c,cos= ,tan= b,cot = a,sec=b, cosec =
<br /> Y
<br /> 6 y ; 0 Given Required
<br /> -7 3 -- a, b A, B,c tan A=b= cot B,c = az+ 2 = a 1 as
<br /> u Gi
<br /> v-i L!: ',�D t l l �✓ `.3
<br /> if, c A,B, Y sin A=Q=cos B,b= c+a)(c—a)
<br /> A,a B, b, c B=90°—A,b =a cot A,c= a
<br /> A.
<br /> sin
<br /> 3 ___ b
<br /> 3 A, b B, a, e B=90'—A,a = b tan A,c= cos A.
<br /> r o - o / , j r A,g B,a, b B-9 Oo—A,a=c sig A,b=c cos A,
<br /> Solution of Oblique Triangles
<br /> Given Required a sin B a em C
<br /> _
<br /> t 1�' tq' ! A, B, a b, c, C b sin A ' d = 180,—(A+B), c = sin
<br /> a ; b sin A
<br /> r A,.a, b B, c, C sin B= a ,C= 180°—(A-i-B),c = a sin C
<br /> ` U sin A
<br /> Dr
<br /> o'r Y a, b, C A, B, c A+B=180°—C,tan (A—B)—(a—b)tan;_(A+J
<br /> a sin C
<br /> a + b
<br /> &. �vV i
<br /> , + b3 sin A
<br /> a+b+c , is-b(s—c
<br /> A, B, C s= ,sin�A
<br /> Iva ,� r7 2 be
<br /> E ;/v 9, 7 2 sin;B=V(x ata ,C=180°—(A+B)
<br /> a+b+c
<br /> ( a, b, c Area 8= 2 area = s s—a s— (8—
<br /> lei.
<br /> —clei. 11 � " � ' �� A, b, a AreabesinA
<br /> ��f area = 2
<br /> 4l
<br /> (n� y `D� J� J 3
<br /> a2 sin B sin C
<br /> 1 / A,B,C,a Area area = 2 sin A
<br /> 0 REDUCTION TO HORIZONTAL
<br /> t / - - Horizontal distance=Slope distance multiplied by the
<br /> <®' _ / 7 cosine of the vertical angle.Thus slope distance=319.4 ft
<br /> IGSY S✓ to Vert. angle=b 101. From Table Page I%.cos b°101=
<br /> 3 n ,� r �apeca m 9969. Horizontal distance=319'4X 9959=31&09 ft
<br /> Horizontal distance also=Slope distance minus slope
<br /> 1 \ 1 4 distance times (1-cosine of vertical angle). With the
<br /> pyo 1 �1 same figures.as in the preceding example,the follow=
<br /> Horizontal distance ing result is obtained.Cosine 6° 0?=.9959.1-.9969=.0041.
<br /> 11
<br /> O ^ p , y, 319,4X.0041=1.31.319.4-1.31=318. ft.
<br /> When the rise is known,the horizontal distance is approximately:-the slope dist-
<br /> ,
<br /> E� 9 7 rJ ance less the square of the size divided is}twice the dope distance. Ms:rise=l4 it,
<br /> slope distance=302.8 ft IldrinaW d 14 X 14
<br /> ` X.3Q28-' 2 8-0. 30228 it.
<br />
|